{"id":9743,"date":"2026-07-25T20:25:11","date_gmt":"2026-07-25T11:25:11","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9743"},"modified":"2026-07-27T15:53:04","modified_gmt":"2026-07-27T06:53:04","slug":"math-abstraction-05-mathematical-structures","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/mathematical-abstraction\/math-abstraction-05-mathematical-structures\/","title":{"rendered":"\uc218\ud559\uc801 \uad6c\uc870\uc640 \ubc94\uc8fc\ub860"},"content":{"rendered":"<p><!-- \uc218\ud559\uc801 \ucd94\uc0c1\ud654 5\ud3b8: \uad6c\uc870\uc758 \uc218\ud559 --><\/p>\n<div class=\"math-abs-series\">\n<p><!-- <a href=\"..\/math-abstraction-04-axiomatic-method\/\">4\ubd80<\/a>\uc5d0\uc11c \uc911\ub300\ud55c \uc9c8\ubb38 \ud558\ub098\ub97c \ub0a8\uae30\uace0 \ub9c8\ubb34\ub9ac\ub418\uc5c8\ub2e4. --> \uad70\uc758 \uacf5\ub9ac, \ud658\uc758 \uacf5\ub9ac, \uccb4\uc758 \uacf5\ub9ac\ucc98\ub7fc \uc11c\ub85c \ub2e4\ub978 \uc774\ub860\uc5d0\uc11c \uc138\uc6cc\uc9c4 \uacf5\ub9ac \uccb4\uacc4\ub4e4\uc744 \ub354 \ub113\uc740 \uad00\uc810\uc5d0\uc11c \ube44\uad50\ud558\uba74 \ubb34\uc5c7\uc744 \ubcfc \uc218 \uc788\uc744\uae4c? 20\uc138\uae30 \uc804\ubc18\uc758 \ub300\uc218\ud559\uc790\ub4e4\uacfc \ubd80\ub974\ubc14\ud0a4\ub294 \uc5ec\ub7ec \uc218\ud559 \ubd84\uc57c\ub97c <span class=\"defined\">\uad6c\uc870<\/span>(structure)\uc640 \uadf8 \uad6c\uc870\ub97c \ubcf4\uc874\ud558\ub294 \ub300\uc751\uc758 \uad00\uc810\uc5d0\uc11c \uc870\uc9c1\ud558\ub294 \ub370 \ud06c\uac8c \uae30\uc5ec\ud588\ub2e4. \ud55c\ud3b8 1940\ub144\ub300\uc5d0 \ub4f1\uc7a5\ud55c \ubc94\uc8fc\ub860\uc740 \uc790\uc5f0\uc131, \ud568\uc790, \uc0ac\uc0c1\uacfc \ubcf4\ud3b8 \uc131\uc9c8\uc744 \uc0c8\ub85c\uc6b4 \uacf5\ud1b5 \uc5b8\uc5b4\ub85c \uc81c\uc2dc\ud588\ub2e4. <!-- \uc774 \ub450 \ud750\ub984\uc5d0\ub294 \ubc00\uc811\ud55c \uad50\ub958\uc640 \uae34\uc7a5\uc774 \uc788\uc5c8\uc9c0\ub9cc, \ubc94\uc8fc\ub860\uc744 \ubd80\ub974\ubc14\ud0a4\uc2dd \uad6c\uc870\ub860\uc758 \ud544\uc5f0\uc801\uc778 \u2018\ub2e4\uc74c \ub2e8\uacc4\u2019\ub77c\uace0 \ub2e8\uc21c\ud654\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. --> \uc774 \uae00\uc5d0\uc11c\ub294 \ub450 \ud750\ub984\uc774 \uac01\uac01 \uc5b4\ub5a4 \ubb38\uc81c\uc5d0\uc11c \ucd9c\ubc1c\ud588\uace0 \uc5b4\ub5bb\uac8c \uc11c\ub85c \ub2e4\ub978 \ucd94\uc0c1\ud654\uc758 \uc5b8\uc5b4\ub97c \uc81c\uacf5\ud588\ub294\uc9c0 \uc0b4\ud3b4\ubcf8\ub2e4.<!-- <a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (1992). \u201cNicolas Bourbaki and the Concept of Mathematical Structure.\u201d Synthese, 92, 315\u2013348.\" href=\"#ref-Corry1992\">[Corry1992]<\/a><a class=\"math-abs-series-ref\" title=\"Eilenberg, S., &amp; Mac Lane, S. (1945). \u201cGeneral Theory of Natural Equivalences.\u201d Transactions of the American Mathematical Society, 58(2), 231\u2013294.\" href=\"#ref-EilenbergMacLane1945\">[EilenbergMacLane1945]<\/a> --><\/p>\n<h4>\ub1cc\ud130, \uacc4\uc0b0\uc744 \uac1c\ub150\uc73c\ub85c \ub300\uccb4\ud558\ub2e4<\/h4>\n<p>1888\ub144, \uc2a4\ubb3c\uc5ec\uc12f \uc0b4\uc758 \ub2e4\ube44\ud2b8 \ud790\ubca0\ub974\ud2b8(David Hilbert)\ub294 \uace0\uc804 \ubd88\ubcc0\ub7c9 \uc774\ub860\uc758 \uc720\ud55c \uc0dd\uc131 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\ub294 \uc0c8\ub85c\uc6b4 \ub17c\uc99d\uc744 \ub9c8\ub828\ud588\ub2e4. \uc774 \uc5f0\uad6c\ub294 1890\ub144 \u201c\ub300\uc218\uc801 \ud615\uc2dd\uc758 \uc774\ub860\uc5d0 \uad00\ud558\uc5ec\u201d(<i>Ueber die Theorie der algebraischen Formen<\/i>)\ub77c\ub294 \ub17c\ubb38\uc73c\ub85c \ucd9c\ud310\ub418\uc5c8\ub2e4. \uc5ec\uae30\uc11c\ub294 \uc11c\ub85c \uad00\ub828\ub418\uc9c0\ub9cc \uad6c\ubcc4\ud574\uc57c \ud558\ub294 \ub450 \uacb0\uacfc\uac00 \ub4f1\uc7a5\ud55c\ub2e4. \ud604\ub300\uc801\uc778 \ud615\ud0dc\uc758 <span class=\"defined\">\ud790\ubca0\ub974\ud2b8 \uae30\uc800 \uc815\ub9ac<\/span>(Hilbert basis theorem)\ub294 \ub1cc\ud130\ud658 \\(R\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\ud56d\uc2dd\ud658 \\(R[x]\\)\ub3c4 \ub1cc\ud130\ud658\uc774\ub77c\ub294 \uba85\uc81c\uc774\uba70, \ud2b9\ud788 \uccb4 \\(k\\) \uc704\uc758 \ub2e4\ud56d\uc2dd\ud658 \\(k[x_1,\\ldots,x_n]\\)\uc758 \ubaa8\ub4e0 \uc544\uc774\ub514\uc5bc\uc774 \uc720\ud55c \uc0dd\uc131\ub428\uc744 \ub73b\ud55c\ub2e4. \ud790\ubca0\ub974\ud2b8\ub294 \uc774\uc640 \uad00\ub828\ub41c \uc544\uc774\ub514\uc5bc\uc758 \uc720\ud55c\uc131 \ub17c\uc99d\uc744 \uc0ac\uc6a9\ud558\uc5ec \uace0\uc804 \ubd88\ubcc0\ub7c9 \uc774\ub860\uc5d0\uc11c \ub2e4\ub8e8\ub358 \ubd88\ubcc0\ub7c9\ud658\uc774 \uc720\ud55c \uac1c\uc758 \ubd88\ubcc0\ub7c9\uc73c\ub85c \uc0dd\uc131\ub41c\ub2e4\ub294 \uc720\ud55c\uc131 \uc815\ub9ac\ub97c \uc5bb\uc5c8\ub2e4. <!-- [\ubd88\ubcc0\ub7c9\ud658\uc758 \uc720\ud55c \uc0dd\uc131 \uc815\ub9ac\uc640 \ub2e4\ud56d\uc2dd \uc544\uc774\ub514\uc5bc\uc5d0 \uad00\ud55c \uae30\uc800 \uc815\ub9ac\ub97c \uac19\uc740 \uc815\ub9ac\ucc98\ub7fc \ud45c\ud604\ud558\uba74 \uc548 \ub41c\ub2e4.]<a class=\"math-abs-series-ref\" title=\"Hilbert, D. (1890). \u201cUeber die Theorie der algebraischen Formen.\u201d Mathematische Annalen, 36, 473\u2013534.\" href=\"#ref-Hilbert1890\">[Hilbert1890]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a> --><\/p>\n<p>\ud790\ubca0\ub974\ud2b8\uc758 \ub17c\uc99d\uc740 \uc720\ud55c\ud55c \uc0dd\uc131\uacc4\uac00 \uc874\uc7ac\ud568\uc744 \ubcf4\uc600\uc9c0\ub9cc, \uc8fc\uc5b4\uc9c4 \ud615\uc2dd\ub4e4\uc5d0 \ub300\ud574 \uadf8 \uc0dd\uc131 \ubd88\ubcc0\ub7c9\ub4e4\uc744 \uc2e4\uc81c\ub85c \uacc4\uc0b0\ud558\ub294 \uc77c\ubc18 \uc808\ucc28\ub97c \uc81c\uc2dc\ud558\uc9c0\ub294 \uc54a\uc558\ub2e4. \uc774\ub294 \uace0\ub974\ub2e8(Paul Gordan)\uc758 \uc0c1\uc9d5\uc801 \uacc4\uc0b0\ubc95\uacfc \ub69c\ub837\uc774 \ub300\ube44\ub418\uc5c8\ub2e4. [\ub2e4\ub9cc \ub2f9\uc2dc\uc758 \ubaa8\ub4e0 \uc218\ud559\uc790\uac00 \uad6c\uc131\uc801 \uacc4\uc0b0\ub9cc\uc744 \uc99d\uba85\uc73c\ub85c \uc778\uc815\ud588\ub2e4\uac70\ub098, \ube44\uad6c\uc131\uc801 \uc874\uc7ac \uc99d\uba85\uc774 \uc774\ub54c \ucc98\uc74c \ub4f1\uc7a5\ud588\ub2e4\uace0 \ub9d0\ud558\ub294 \uac83\uc740 \uacfc\uc7a5\uc774\ub2e4.<sup class=\"modern-footnotes-footnote \" data-mfn=\"1\" data-mfn-post-scope=\"00000000000003e50000000000000000_9743\"><a href=\"javascript:void(0)\"  role=\"button\" aria-pressed=\"false\" aria-describedby=\"mfn-content-00000000000003e50000000000000000_9743-1\">1<\/a><\/sup><span id=\"mfn-content-00000000000003e50000000000000000_9743-1\" role=\"tooltip\" class=\"modern-footnotes-footnote__note\" tabindex=\"0\" data-mfn=\"1\">\u201c\uc774\uac83\uc740 \uc218\ud559\uc774 \uc544\ub2c8\ub77c \uc2e0\ud559\uc774\ub2e4\u201d\ub77c\ub294 \ubb38\uad6c\ub294 \uace0\ub974\ub2e8\uc774 \ud790\ubca0\ub974\ud2b8\uc758 \ub17c\uc99d\uc744 \ubcf4\uace0 \ud588\ub2e4\uace0 \ub110\ub9ac \uc804\ud574\uc9c0\uc9c0\ub9cc, \ud604\uc7ac \uc54c\ub824\uc9c4 \ub2f9\uc2dc\uc758 \uc2ec\uc0ac\ubcf4\uace0\ub098 \uc11c\uc2e0\uc5d0\uc11c\ub294 \uadf8 \uc815\ud655\ud55c \ubb38\uad6c\uc640 \ubc1c\uc5b8 \uc0c1\ud669\uc774 \ud655\uc778\ub418\uc9c0 \uc54a\ub294\ub2e4. \uc774 \ub9d0\uc740 \ud6c4\ub300\uc5d0 \ud615\uc131\ub41c \uc77c\ud654\ub77c\ub294 \ub2e8\uc11c\ub97c \ubd99\uc5ec \uc778\uc6a9\ud574\uc57c \ud55c\ub2e4. \uace0\ub974\ub2e8\uc740 \ud790\ubca0\ub974\ud2b8 \ub17c\ubb38\uc758 \ub17c\uc99d\uacfc \uc81c\uc2dc \ubc29\uc2dd\uc5d0 \ube44\ud310\uc801\uc778 \uc758\uacac\uc744 \ub0b4\uae30\ub3c4 \ud588\uc9c0\ub9cc, \uc774\ud6c4 \uadf8 \ubc29\ubc95\uc744 \ubc1b\uc544\ub4e4\uc5ec \ud65c\uc6a9\ud588\ub2e4. \ub530\ub77c\uc11c \ub450 \uc0ac\ub78c\uc758 \uad00\uacc4\ub97c \u2018\uacc4\uc0b0\uc801 \uc218\ud559\uacfc \ucd94\uc0c1\uc801 \uc218\ud559\uc758 \ub2e8\uc21c\ud55c \uc801\ub300\u2019\ub85c \ubb18\uc0ac\ud558\ub294 \uac83\ub3c4 \uc815\ud655\ud558\uc9c0 \uc54a\ub2e4.<a class=\"math-abs-series-ref\" title=\"McLarty, C. (2012). \u201cHilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics.\u201d In A. Doxiadis &amp; B. Mazur (Eds.), Circles Disturbed: The Interplay of Mathematics and Narrative, 105\u2013129. Princeton University Press.\" href=\"#ref-McLarty2012\">[McLarty2012]<\/a><\/span>] \ud790\ubca0\ub974\ud2b8\uc758 \ub17c\uc99d\uc758 \uc5ed\uc0ac\uc801 \uc911\uc694\uc131\uc740 \ubcf5\uc7a1\ud55c \uc0dd\uc131\uc6d0\uc744 \uc77c\uc77c\uc774 \uacc4\uc0b0\ud558\ub294 \ub300\uc2e0 \uc544\uc774\ub514\uc5bc\uc758 \uc720\ud55c\uc131\uc774\ub77c\ub294 \uc77c\ubc18 \uba85\uc81c\ub97c \ud1b5\ud574 \uc874\uc7ac\ub97c \ubcf4\uc600\ub2e4\ub294 \ub370 \uc788\ub2e4.<a class=\"math-abs-series-ref\" title=\"Hilbert, D. (1890). \u201cUeber die Theorie der algebraischen Formen.\u201d Mathematische Annalen, 36, 473\u2013534.\" href=\"#ref-Hilbert1890\">[Hilbert1890]<\/a><a class=\"math-abs-series-ref\" title=\"McLarty, C. (2012). \u201cHilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics.\u201d In A. Doxiadis &amp; B. Mazur (Eds.), Circles Disturbed: The Interplay of Mathematics and Narrative, 105\u2013129. Princeton University Press.\" href=\"#ref-McLarty2012\">[McLarty2012]<\/a><\/p>\n<p>\uc774\ub7ec\ud55c \uc720\ud55c\uc131 \uc870\uac74\uc744 \uc77c\ubc18\uc801\uc778 \uac00\ud658\ub300\uc218\uc758 \uc911\uc2ec \uc6d0\ub9ac\ub85c \ubc1c\uc804\uc2dc\ud0a8 \uc778\ubb3c \uac00\uc6b4\ub370 \uac00\uc7a5 \uc911\uc694\ud55c \uc218\ud559\uc790\uac00 \uc5d0\ubbf8 \ub1cc\ud130(Emmy Noether)\uc774\ub2e4. \ub1cc\ud130\ub294 1921\ub144 \ub17c\ubb38 \u201c\ud658 \uc601\uc5ed\uc5d0\uc11c\uc758 \uc544\uc774\ub514\uc5bc \uc774\ub860\u201d(<i>Idealtheorie in Ringbereichen<\/i>)\uc5d0\uc11c \ub370\ub370\ud0a8\ud2b8\u00b7\ud790\ubca0\ub974\ud2b8\u00b7\ub77c\uc2a4\ucee4\u00b7\ub9e4\ucf5c\ub9ac \ub4f1\uc758 \uc544\uc774\ub514\uc5bc \uc774\ub860\uc744 \uc77c\ubc18\uc801\uc778 \uac00\ud658\ud658\uc758 \uc5b8\uc5b4\ub85c \uc7ac\uad6c\uc131\ud588\ub2e4. \ud604\ub300\uc801\uc778 \ud45c\ud604\uc73c\ub85c, \uac00\ud658\ud658 \\(R\\)\uc758 \ubd80\ubd84\uc9d1\ud569 \\(I\\)\uac00 \ub367\uc148\uc5d0 \uad00\ud574 \ubd80\ubd84\uad70\uc744 \uc774\ub8e8\uace0 \ubaa8\ub4e0 \\(r\\in R\\)\uc640 \\(x\\in I\\)\uc5d0 \ub300\ud574 \\(rx\\in I\\)\ub97c \ub9cc\uc871\ud558\uba74 \\(I\\)\ub97c \\(R\\)\uc758 <span class=\"defined\">\uc544\uc774\ub514\uc5bc<\/span>(ideal)\uc774\ub77c\uace0 \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Noether, E. (1921). \u201cIdealtheorie in Ringbereichen.\u201d Mathematische Annalen, 83, 24\u201366. \uc601\uc5b4 \ubc88\uc5ed: arXiv:1401.2577.\" href=\"#ref-Noether1921\">[Noether1921]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><\/p>\n<p>\ub1cc\ud130\uac00 \uc911\uc2ec\uc801\uc73c\ub85c \uc0ac\uc6a9\ud55c \uc720\ud55c\uc131 \uc870\uac74\uc740 \uc544\uc774\ub514\uc5bc\ub4e4\uc758 \ubaa8\ub4e0 \uc624\ub984\uc0ac\uc2ac<br \/>\n\\[<br \/>\nI_1\\subseteq I_2\\subseteq I_3\\subseteq\\cdots<br \/>\n\\]<br \/>\n\uc774 \uc5b4\ub290 \ub2e8\uacc4\ubd80\ud130 \uc548\uc815\ub41c\ub2e4\ub294 \uac83\uc774\ub2e4. \uc989 \uc5b4\ub5a4 \\(N\\)\uc774 \uc874\uc7ac\ud558\uc5ec<br \/>\n\\[<br \/>\nI_N=I_{N+1}=I_{N+2}=\\cdots<br \/>\n\\]<br \/>\n\uac00 \ub418\uc5b4\uc57c \ud55c\ub2e4. \uc774\ub97c <span class=\"defined\">\uc624\ub984\uc0ac\uc2ac\uc870\uac74<\/span>(ascending chain condition, ACC)\uc774\ub77c\uace0 \ud55c\ub2e4. \uc624\ub298\ub0a0 \uac00\ud658\ud658 \\(R\\)\uc774 \uc774 \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\uba74 \\(R\\)\uc744 <span class=\"defined\">\ub1cc\ud130\ud658<\/span>(Noetherian ring)\uc774\ub77c\uace0 \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Noether, E. (1921). \u201cIdealtheorie in Ringbereichen.\u201d Mathematische Annalen, 83, 24\u201366. \uc601\uc5b4 \ubc88\uc5ed: arXiv:1401.2577.\" href=\"#ref-Noether1921\">[Noether1921]<\/a><a class=\"math-abs-series-ref\" title=\"The Stacks Project Authors. \u201cNoetherian rings.\u201d The Stacks Project, Tag 00FM.\" href=\"#ref-StacksProject\">[StacksProject]<\/a><\/p>\n<p>[\uac00\ud658\ud658 \\(R\\)\uc5d0 \ub300\ud558\uc5ec \u2018\uc544\uc774\ub514\uc5bc\uc758 \uc624\ub984\uc0ac\uc2ac\uc870\uac74\u2019\uacfc \u2018\\(R\\)\uc758 \ubaa8\ub4e0 \uc544\uc774\ub514\uc5bc\uc774 \uc720\ud55c \uc0dd\uc131\ub41c\ub2e4\u2019\ub294 \uc870\uac74\uc740 \uc11c\ub85c \ub3d9\uce58\ub2e4. \ubaa8\ub4e0 \uc544\uc774\ub514\uc5bc\uc774 \uc720\ud55c \uc0dd\uc131\uc774\uace0 \\(I_1\\subseteq I_2\\subseteq\\cdots\\)\uc774\uba74 \\(I=\\bigcup_n I_n\\)\ub3c4 \uc544\uc774\ub514\uc5bc\uc774\ub2e4. \\(I\\)\uc758 \uc720\ud55c\ud55c \uc0dd\uc131\uc6d0\ub4e4\uc740 \ubaa8\ub450 \uc5b4\ub5a4 \ud558\ub098\uc758 \\(I_N\\)\uc5d0 \ub4e4\uc5b4\uac00\ubbc0\ub85c \\(I=I_N\\)\uc774\uace0 \uc0ac\uc2ac\uc740 \uc548\uc815\ub41c\ub2e4. \ubc18\ub300\ub85c \uc720\ud55c \uc0dd\uc131\ub418\uc9c0 \uc54a\ub294 \uc544\uc774\ub514\uc5bc \\(I\\)\uac00 \uc788\ub2e4\uba74 \\(x_1\\in I\\)\ub97c \ud0dd\ud558\uace0, \uc774\ubbf8 \ud0dd\ud55c \uc6d0\uc18c\ub4e4\uc774 \uc0dd\uc131\ud558\ub294 \uc544\uc774\ub514\uc5bc \ubc16\uc5d0\uc11c \\(x_2,x_3,\\ldots\\)\ub97c \ucc28\ub840\ub85c \uace8\ub77c<br \/>\n\\[<br \/>\n(x_1)\\subsetneq(x_1,x_2)\\subsetneq(x_1,x_2,x_3)\\subsetneq\\cdots<br \/>\n\\]<br \/>\n\ub77c\ub294 \uc548\uc815\ub418\uc9c0 \uc54a\ub294 \uc624\ub984\uc0ac\uc2ac\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<a class=\"math-abs-series-ref\" title=\"The Stacks Project Authors. \u201cNoetherian rings.\u201d The Stacks Project, Tag 00FM.\" href=\"#ref-StacksProject\">[StacksProject]<\/a>]<\/p>\n<p>\ub1cc\ud130\uc758 1921\ub144 \ub17c\ubb38\uc774 \ubcf4\uc5ec \uc900 \ub300\ud45c\uc801\uc778 \uc131\uacfc\ub294 \ub77c\uc2a4\ucee4\uc758 \ub2e4\ud56d\uc2dd \uc544\uc774\ub514\uc5bc \ubd84\ud574 \uc815\ub9ac\ub97c \uc77c\ubc18\ud654\ud55c \ub77c\uc2a4\ucee4\u2013\ub1cc\ud130 \uc815\ub9ac\ub2e4. \uc774\uc5d0 \ub530\ub974\uba74 \uac00\ud658 \ub1cc\ud130\ud658\uc758 \ubaa8\ub4e0 \uace0\uc720 \uc544\uc774\ub514\uc5bc\uc740 \uc720\ud55c \uac1c\uc758 \uc77c\ucc28 \uc544\uc774\ub514\uc5bc(primary ideal)\uc758 \uad50\uc9d1\ud569\uc73c\ub85c \ud45c\ud604\ub41c\ub2e4.<!-- [mfn]\ub530\ub77c\uc11c \ub1cc\ud130\uac00 \ub2e8 \ud558\ub098\uc758 \uc870\uac74\uc73c\ub85c \ub300\uc218\uc801 \uc815\uc218\ub860\uc758 \ubaa8\ub4e0 \uac1c\ubcc4 \uc815\ub9ac\ub97c \uc774\ub04c\uc5b4 \ub0c8\ub2e4\uace0 \ud558\uae30\ubcf4\ub2e4, \uc624\ub984\uc0ac\uc2ac\uc870\uac74\uc744 \uc774\uc6a9\ud574 \uc544\uc774\ub514\uc5bc \ubd84\ud574 \uc774\ub860\uc744 \uad11\ubc94\uc704\ud55c \uac00\ud658\ud658\uc5d0 \uc801\uc6a9\ud560 \uc218 \uc788\ub294 \uc77c\ubc18 \uc815\ub9ac\ub85c \ubc14\uafb8\uc5c8\ub2e4\uace0 \ub9d0\ud558\ub294 \ud3b8\uc774 \uc815\ud655\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Noether, E. (1921). \u201cIdealtheorie in Ringbereichen.\u201d Mathematische Annalen, 83, 24\u201366. \uc601\uc5b4 \ubc88\uc5ed: arXiv:1401.2577.\" href=\"#ref-Noether1921\">[Noether1921]<\/a>[\/mfn] --><\/p>\n<p>\ub1cc\ud130\ub294 \uc790\uc2e0\uc758 \uc5f0\uad6c\uac00 \ub370\ub370\ud0a8\ud2b8\uc758 \uc544\uc774\ub514\uc5b4\uc640 \uae4a\uc774 \uc5f0\uacb0\ub418\uc5b4 \uc788\uc74c\uc744 \uac15\uc870\ud588\ub2e4. \ub370\ub370\ud0a8\ud2b8\uc758 \uc5f0\uad6c\uc5d0 \uc0ac\uc0c1\uacfc \uc544\uc774\ub514\uc5bc\uc758 \uad00\uacc4\uc5d0 \uad00\ud55c \uac15\ud55c \uad6c\uc870\uc801 \uad00\uc810\uc774 \uc788\uc5c8\uc73c\uba70, \ub1cc\ud130\ub294 \ub370\ub370\ud0a8\ud2b8\uc758 \uc5f0\uad6c\ub97c \ud3ec\ud568\ud558\uc5ec \ud790\ubca0\ub974\ud2b8, \ub77c\uc2a4\ucee4, \ub9e4\ucf5c\ub9ac \ub4f1 \uc5ec\ub7ec \uc5f0\uad6c \uc804\ud1b5\uc744 \uc885\ud569\ud574 \uc77c\ubc18 \uac00\ud658\ub300\uc218\uc758 \uc5b8\uc5b4\ub85c \ubc1c\uc804\uc2dc\ucf30\ub2e4.<a class=\"math-abs-series-ref\" title=\"van der Waerden, B. L. (1975). \u201cOn the Sources of My Book Moderne Algebra.\u201d Historia Mathematica, 2(1), 31\u201340.\" href=\"#ref-VanDerWaerden1975\">[VanDerWaerden1975]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><\/p>\n<p><!--\n\n\n<p>[\u201cEs steht alles schon bei Dedekind\u201d, \uc989 \u201c\ubaa8\ub4e0 \uac83\uc740 \uc774\ubbf8 \ub370\ub370\ud0a8\ud2b8\uc5d0 \ub4e4\uc5b4 \uc788\ub2e4\u201d\ub77c\ub294 \ub9d0\uc740 \ucd9c\ucc98\uac00 \uc804\ud600 \uc5c6\ub294 \uc804\uc124\uc740 \uc544\ub2c8\ub2e4. \ub1cc\ud130\uc758 \uac15\uc758\ub97c \uc9c1\uc811 \ub4e4\uc5c8\ub358 \ud310\ub370\ub974\ubc14\ub974\ub358\uc740 1975\ub144 \ud68c\uace0 \ub17c\ubb38 \u201cOn the Sources of My Book Moderne Algebra\u201d\uc5d0\uc11c \uc774 \ub9d0\uc744 \ub1cc\ud130\uc5d0\uac8c \uadc0\uc18d\ud588\ub2e4. \ubc1c\uc5b8 \ub2f9\uc2dc\uc758 \ub179\ucde8\ub294 \uc544\ub2c8\ubbc0\ub85c \uc815\ud655\ud55c \uc2dc\uc810\uacfc \ub9e5\ub77d\uae4c\uc9c0 \ud655\uc815\ud560 \uc218\ub294 \uc5c6\uc9c0\ub9cc, \uac00\uae4c\uc6b4 \uc81c\uc790\uc758 \ud68c\uace0 \uc99d\uc5b8\uc73c\ub85c\ub294 \uc778\uc6a9\ud560 \uc218 \uc788\ub2e4.<a class=\"math-abs-series-ref\" title=\"van der Waerden, B. L. (1975). \u201cOn the Sources of My Book Moderne Algebra.\u201d Historia Mathematica, 2(1), 31\u201340.\" href=\"#ref-VanDerWaerden1975\">[VanDerWaerden1975]<\/a>]<\/p>\n\n\n--><\/p>\n<h4>\uad6c\uc870\uac00 \ubaa9\ucc28\uac00 \ub418\ub2e4<\/h4>\n<p>\ud310\ub370\ub974\ubc14\ub974\ub358(Bartel van der Waerden)\uc740 1924\ub144 \uad34\ud305\uac90\uc5d0\uc11c \ub1cc\ud130\uc758 \uac15\uc758\uc640 \uc5f0\uad6c \ud658\uacbd\uc744 \uc811\ud588\uace0, 1926\ub144\uc5d0\ub294 \ud568\ubd80\ub974\ud06c\uc5d0\uc11c \uc5d0\ubc00 \uc544\ub974\ud2f4(Emil Artin)\uc758 \ub300\uc218\ud559 \uac15\uc758\ub97c \ub4e4\uc5c8\ub2e4. \uadf8\uac00 1930\ub144\uacfc 1931\ub144\uc5d0 \ub450 \uad8c\uc73c\ub85c \ucd9c\ud310\ud55c \u201c\ud604\ub300 \ub300\uc218\ud559\u201d(<i>Moderne Algebra<\/i>)\uc758 \ubd80\uc81c\ub294 \uc774 \ucc45\uc774 \uc544\ub974\ud2f4\uacfc \ub1cc\ud130\uc758 \uac15\uc758\ub97c \uc774\uc6a9\ud574 \uc791\uc131\ub418\uc5c8\uc74c\uc744 \uba85\uc2dc\ud55c\ub2e4. \ud310\ub370\ub974\ubc14\ub974\ub358 \uc790\uc2e0\uc740 \ucc45\uc774 \uc544\ub974\ud2f4\uc758 \uac15\uc758 \ub178\ud2b8\uc5d0\uc11c \ucd9c\ubc1c\ud588\uc9c0\ub9cc \uc5ec\ub7ec \ucc28\ub840\uc758 \uc7ac\uc791\uc131\uacfc \ub2e4\ub978 \uac15\uc758\u00b7\ub17c\ubb38\u00b7\uc790\uc2e0\uc758 \uc5f0\uad6c\ub97c \ubc18\uc601\ud558\uba74\uc11c \uc6d0\ub798 \uac15\uc758\uc640 \uc0c1\ub2f9\ud788 \ub2ec\ub77c\uc84c\ub2e4\uace0 \ud68c\uace0\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"van der Waerden, B. L. (1975). \u201cOn the Sources of My Book Moderne Algebra.\u201d Historia Mathematica, 2(1), 31\u201340.\" href=\"#ref-VanDerWaerden1975\">[VanDerWaerden1975]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><\/p>\n<p>\uc218\ud559\uc0ac \uc5f0\uad6c\uc5d0\uc11c\ub294 \uc774 \ucc45\uc744 \ub300\uc218\ud559\uc758 \uc5ec\ub7ec \ubd84\uc57c\ub97c \uc9d1\ud569\ub860\uc801\u00b7\uacf5\ub9ac\uc801 \uad00\uc810\uc5d0\uc11c \ud558\ub098\uc758 \ud1b5\uc77c\ub41c \uc804\uccb4\ub85c \uc81c\uc2dc\ud55c \ucd5c\ucd08\uc758 \uccb4\uacc4\uc801\uc778 \uad50\uacfc\uc11c \uac00\uc6b4\ub370 \uac00\uc7a5 \uc601\ud5a5\ub825 \uc788\ub294 \uc800\uc220\ub85c \ud3c9\uac00\ud55c\ub2e4. <!-- \ub2e4\ub9cc \uc2e4\uc81c \ubaa9\ucc28\uac00 \u2018\uad70\u00b7\ud658\u00b7\uccb4\u2019\ub77c\ub294 \uc138 \uc7a5\ub9cc\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uac83\uc740 \uc544\ub2c8\ub2e4.  --> \uc81c1\uad8c\uc740 \uc218\uc640 \uc9d1\ud569\uc744 \ub2e4\ub8ec \ub4a4 \uad70, \ud658\uacfc \uccb4, \ub2e4\ud56d\uc2dd, \uccb4\ub860, \uac08\ub8e8\uc544 \uc774\ub860 \ub4f1\uc744 \uc804\uac1c\ud588\uace0, \uc81c2\uad8c\uc740 \uc544\uc774\ub514\uc5bc \uc774\ub860\uacfc \ucd08\ubcf5\uc18c\uc218 \uccb4\uacc4 \ub4f1\uc744 \ud3ec\ud568\ud588\ub2e4. \ud2b9\ud788 \ub2e4\uc74c\uacfc \uac19\uc740 \uad6c\uc870\uac00 \ucc45 \uc804\uccb4\ub97c \uc870\uc9c1\ud558\ub294 \uacf5\ud1b5 \uc5b8\uc5b4\uac00 \ub418\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"van der Waerden, B. L. (1975). \u201cOn the Sources of My Book Moderne Algebra.\u201d Historia Mathematica, 2(1), 31\u201340.\" href=\"#ref-VanDerWaerden1975\">[VanDerWaerden1975]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><\/p>\n<ul>\n<li>\uad70(group)<\/li>\n<li>\ud658(ring)<\/li>\n<li>\uccb4(field)<\/li>\n<\/ul>\n<p>\uc815\uc218, \ub2e4\ud56d\uc2dd, \ud589\ub82c\uacfc \uac19\uc740 \uad6c\uccb4\uc801\uc778 \ub300\uc0c1\ub4e4\uc740 \uc774 \uad6c\uc870\ub4e4\uc758 \uc911\uc694\ud55c \uc0ac\ub840\ub85c \uc11c\ub85c \ube44\uad50\ub420 \uc218 \uc788\uac8c \ub418\uc5c8\ub2e4. <!-- \uadf8\ub7ec\ub098 \uadf8 \ub300\uc0c1\ub4e4\uc758 \uace0\uc720\ud55c \uc0b0\uc220\uc801\u00b7\uae30\ud558\ud559\uc801 \uc131\uc9c8\uc774 \ubaa8\ub450 \ubd80\ucc28\uc801\uc778 \uc815\ubcf4\ub85c \uaca9\ud558\ub418\uc5c8\ub2e4\uace0 \ub9d0\ud560 \uc218\ub294 \uc5c6\ub2e4. --> \uad6c\uc870\uc801 \uad00\uc810\uc740 \uad6c\uccb4\uc801 \ub300\uc0c1\uc758 \uc5f0\uad6c\ub97c \uc5c6\uc564 \uac83\uc774 \uc544\ub2c8\ub77c \uc11c\ub85c \ub2e4\ub978 \ub300\uc0c1\uc5d0 \uacf5\ud1b5\uc73c\ub85c \uc801\uc6a9\ub418\ub294 \uc815\uc758\uc640 \uc815\ub9ac\ub97c \ubd84\ub9ac\ud574 \ub0c8\ub2e4. \u201cModerne Algebra\u201d\ub294 \ud6c4\ub300 \ub300\uc218\ud559 \uad50\uc7ac\uc758 \uc11c\uc220 \uc591\uc2dd\uc744 \uc815\ucc29\uc2dc\ud0a4\ub294 \ub370 \ud06c\uac8c \uae30\uc5ec\ud588\ub2e4. <!-- [mfn]\uc624\ub298\ub0a0\uc758 \ubaa8\ub4e0 \u2018\uad70\ub860\u2013\ud658\ub860\u2013\uccb4\ub860\u2019 \uad50\uc721\uacfc\uc815\uc774 \uc624\uc9c1 \uc774 \ucc45 \ud558\ub098\uc5d0\uc11c \ube44\ub86f\ub418\uc5c8\ub2e4\uace0 \ub2e8\uc815\ud558\uae30\ubcf4\ub2e4\ub294, \uc774 \ucc45\uc774 \uadf8\ub7ec\ud55c \uad6c\uc870\uc801 \ud3b8\uc81c\ub97c \ub110\ub9ac \ud655\uc0b0\uc2dc\ud0a8 \uacb0\uc815\uc801\uc778 \ubcf8\ubcf4\uae30\uc600\ub2e4\uace0 \ud45c\ud604\ud558\ub294 \uac83\uc774 \uc801\uc808\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"van der Waerden, B. L. (1975). \u201cOn the Sources of My Book Moderne Algebra.\u201d Historia Mathematica, 2(1), 31\u201340.\" href=\"#ref-VanDerWaerden1975\">[VanDerWaerden1975]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a>[\/mfn] --><\/p>\n<h4>\ubd80\ub974\ubc14\ud0a4, \uad6c\uc870\ub97c \uc131\ubb38\ud654\ud558\ub2e4<\/h4>\n<p>1934\ub144 \ub9d0 \uc559\ub4dc\ub808 \ubca0\uc720(Andr\u00e9 Weil), \uc559\ub9ac \uce74\ub974\ud0d5(Henri Cartan), \ud074\ub85c\ub4dc \uc288\ubc1c\ub808(Claude Chevalley), \uc7a5 \ub378\uc0ac\ub974\ud2b8(Jean Delsarte), \uc7a5 \ub514\uc678\ub3c4\ub124(Jean Dieudonn\u00e9), \ub974\ub124 \ub4dc \ud3ec\uc140(Ren\u00e9 de Possel) \ub4f1 \ud504\ub791\uc2a4\uc758 \uc80a\uc740 \uc218\ud559\uc790\ub4e4\uc740 \ub0a1\uc740 \ud504\ub791\uc2a4 \ub300\ud559 \ud574\uc11d\ud559 \uad50\uc7ac\ub97c \ub300\uc2e0\ud560 \uacf5\ub3d9 \uad50\uacfc\uc11c\ub97c \ub17c\uc758\ud558\uae30 \uc2dc\uc791\ud588\ub2e4. 1935\ub144 \uccab \uacf5\uc2dd \ud68c\ud569\uc744 \uac70\uce58\uba70 \uc774\ub4e4\uc740 \ub2c8\ucf5c\ub77c \ubd80\ub974\ubc14\ud0a4(Nicolas Bourbaki)\ub77c\ub294 \uacf5\ub3d9 \ud544\uba85\uc744 \ucc44\ud0dd\ud588\ub2e4. \ucc98\uc74c\ubd80\ud130 \u2018\uc218\ud559 \uc804\uccb4\ub97c \uc644\uc131\ub41c \ud558\ub098\uc758 \uccb4\uacc4\ub85c \ub2e4\uc2dc \uc138\uc6b4\ub2e4\u2019\ub294 \uacc4\ud68d\uc774 \uc788\uc5c8\ub358 \uac83\uc740 \uc544\ub2c8\ub2e4. \ucd9c\ubc1c\uc810\uc740 \ud604\ub300\uc801\uc778 \ud574\uc11d\ud559 \uad50\uc7ac\uc600\uace0, \ub17c\uc758\uc640 \uc7ac\uc791\uc131\uc744 \uac70\uce58\uba74\uc11c \uc9d1\ud569\ub860\u00b7\ub300\uc218\ud559\u00b7\uc704\uc0c1\uc218\ud559 \ub4f1 \ud574\uc11d\ud559\uc758 \uc804\uc81c\uac00 \ub418\ub294 \ubd84\uc57c\ub85c \ubc94\uc704\uac00 \ud655\ub300\ub418\uc5c8\ub2e4. \uadf8 \uacb0\uacfc\ubb3c\uc774 \uc7a5\uae30\uac04\uc5d0 \uac78\uccd0 \ucd9c\ud310\ub41c \ucd1d\uc11c \u201c\uc218\ud559 \uc6d0\ub860\u201d(<i>\u00c9l\u00e9ments de math\u00e9matique<\/i>)\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Association des collaborateurs et collaboratrices de Nicolas Bourbaki. \u201cFounding Members.\u201d \ubd80\ub974\ubc14\ud0a4 \ud611\ud68c \uacf5\uc2dd \uc0ac\uc774\ud2b8.\" href=\"#ref-BourbakiAssociation\">[BourbakiAssociation]<\/a><a class=\"math-abs-series-ref\" title=\"Beaulieu, L. (1993). \u201cA Parisian Caf\u00e9 and Ten Proto-Bourbaki Meetings (1934\u20131935).\u201d The Mathematical Intelligencer, 15, 27\u201335.\" href=\"#ref-Beaulieu1993\">[Beaulieu1993]<\/a><\/p>\n<p>[\ub2c8\ucf5c\ub77c \ubd80\ub974\ubc14\ud0a4\ub294 \uc2e4\uc874\ud558\ub294 \ud55c \uba85\uc758 \uc218\ud559\uc790\uac00 \uc544\ub2c8\ub77c 1934\u20131935\ub144\uc5d0 \uacb0\uc131\ub41c \uc218\ud559\uc790 \uc9d1\ub2e8\uc774 \uacf5\ub3d9 \uc800\uc220\uc5d0 \uc0ac\uc6a9\ud55c \ud544\uba85\uc774\ub2e4. \ucc38\uc5ec\uc790\ub294 \uc2dc\uae30\uc5d0 \ub530\ub77c \ubc14\ub00c\uc5c8\uc73c\uba70, \ud2b9\uc815 \uc815\ub9ac\ub098 \uc7a5\uc744 \ud55c \uac1c\uc778\uc758 \uc800\uc791\uc73c\ub85c \uadc0\uc18d\ud558\uc9c0 \uc54a\ub294 \uac83\uc774 \uc774 \uc9d1\ub2e8\uc758 \uc6d0\uce59\uc774\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Association des collaborateurs et collaboratrices de Nicolas Bourbaki. \u201cFounding Members.\u201d \ubd80\ub974\ubc14\ud0a4 \ud611\ud68c \uacf5\uc2dd \uc0ac\uc774\ud2b8.\" href=\"#ref-BourbakiAssociation\">[BourbakiAssociation]<\/a><a class=\"math-abs-series-ref\" title=\"Beaulieu, L. (1993). \u201cA Parisian Caf\u00e9 and Ten Proto-Bourbaki Meetings (1934\u20131935).\u201d The Mathematical Intelligencer, 15, 27\u201335.\" href=\"#ref-Beaulieu1993\">[Beaulieu1993]<\/a>]<\/p>\n<p>\ubd80\ub974\ubc14\ud0a4\ub294 \uacf5\ub9ac\uc801\u00b7\uad6c\uc870\uc801 \uad00\uc810\uc744 \ub300\uc218\ud559\ubfd0 \uc544\ub2c8\ub77c \uc5ec\ub7ec \uc218\ud559 \ubd84\uc57c\ub97c \uc870\uc9c1\ud558\ub294 \uc6d0\ub9ac\ub85c \uc81c\uc2dc\ud588\ub2e4. 1948\ub144 \ud504\ub791\uc2a4\uc5b4\ub85c \ubc1c\ud45c\ub418\uace0 1950\ub144 \uc601\uc5b4\ub85c \ubc88\uc5ed\ub41c \uc5d0\uc138\uc774 \u201c\uc218\ud559\uc758 \uac74\ucd95\u201d(<i>L\u2019architecture des math\u00e9matiques<\/i>)\uc5d0\uc11c \ubd80\ub974\ubc14\ud0a4\ub294 \uc218\ud559\uc758 \uc911\uc2ec\uc5d0 \uc788\ub294 \uba87 \uac00\uc9c0 \ud070 \uad6c\uc870 \uc720\ud615\uc744 <span class=\"defined\">\ubaa8\uad6c\uc870<\/span>(structures m\u00e8res, mother structures)\ub77c\uace0 \ubd80\ub974\uba70 \ub2e4\uc74c \uc138 \uc720\ud615\uc744 \uc608\ub85c \ub4e4\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Bourbaki, N. (1950). \u201cThe Architecture of Mathematics.\u201d The American Mathematical Monthly, 57(4), 221\u2013232.\" href=\"#ref-Bourbaki1950\">[Bourbaki1950]<\/a><\/p>\n<p><!--\n[mfn]\uc774 \uad00\uc810\uc740 \ud790\ubca0\ub974\ud2b8\uc758 \uacf5\ub9ac\uc801 \ubc29\ubc95\uacfc \ubd84\uba85\ud55c \uce5c\uc5f0\uc131\uc774 \uc788\uc9c0\ub9cc, \u2018\ud790\ubca0\ub974\ud2b8\uac00 \uae30\ud558\ud559\uc5d0\uc11c \uc218\ud589\ud55c \uc554\ubb35\uc801 \uc815\uc758\ub97c \ubd80\ub974\ubc14\ud0a4\uac00 \uc218\ud559 \uc804\uccb4\ub85c \uadf8\ub300\ub85c \ud655\ub300\ud588\ub2e4\u2019\ub294 \ubb38\uc7a5\uc740 \uc5ed\uc0ac\uc801 \uc0ac\uc2e4 \uc790\uccb4\ub77c\uae30\ubcf4\ub2e4 \ud574\uc11d\uc801\uc778 \uc694\uc57d\uc774\ub2e4. \ub610\ud55c 1948\ub144 \uc120\uc5b8\ubb38\uc758 \ubaa8\uad6c\uc870 \ub3c4\uc2dd\uc740 \u201c\uc9d1\ud569\ub860\u201d\uc5d0\uc11c \uc804\uac1c\ub41c \ubd80\ub974\ubc14\ud0a4\uc758 \ud615\uc2dd\uc801 \uad6c\uc870 \uc815\uc758\uc640 \ub3d9\uc77c\ud558\uc9c0 \uc54a\ub2e4. \uc774 \ub3c4\uc2dd\uc740 \uac1c\ub7b5\uc801\uc778 \uc548\ub0b4\ub3c4\uc774\uc9c0 \uad6c\uc870\ub97c \uc14b\uc73c\ub85c \uc644\uacb0\ud558\uc5ec \ubd84\ub958\ud55c \uc815\ub9ac\uac00 \uc544\ub2c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Corry, L. (2004). Modern Algebra and the Rise of Mathematical Structures (2nd rev. ed.). Birkh\u00e4user.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><a class=\"math-abs-series-ref\" title=\"Bourbaki, N. (1950). \u201cThe Architecture of Mathematics.\u201d The American Mathematical Monthly, 57(4), 221\u2013232.\" href=\"#ref-Bourbaki1950\">[Bourbaki1950]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (1992). \u201cNicolas Bourbaki and the Concept of Mathematical Structure.\u201d Synthese, 92, 315\u2013348.\" href=\"#ref-Corry1992\">[Corry1992]<\/a>][\/mfn]\n--><\/p>\n<ul>\n<li><strong>\ub300\uc218\uc801 \uad6c\uc870<\/strong>: \ud558\ub098 \uc774\uc0c1\uc758 \ud569\uc131\ubc95\uce59 \ub610\ub294 \uc5f0\uc0b0\uacfc \uadf8\uac83\ub4e4\uc774 \ub9cc\uc871\ud558\ub294 \uacf5\ub9ac\ub85c \uaddc\uc815\ub418\ub294 \uad6c\uc870\ub2e4.<\/li>\n<li><strong>\uc21c\uc11c \uad6c\uc870<\/strong>: \uc6d0\uc18c\ub4e4 \uc0ac\uc774\uc758 \uc21c\uc11c \uad00\uacc4\uc640 \uadf8 \uad00\uacc4\uac00 \ub9cc\uc871\ud558\ub294 \uacf5\ub9ac\ub85c \uaddc\uc815\ub418\ub294 \uad6c\uc870\ub2e4.<\/li>\n<li><strong>\uc704\uc0c1 \uad6c\uc870<\/strong>: \uadfc\ubc29\u00b7\uadf9\ud55c\u00b7\uc5f0\uc18d\uc131\uc758 \uc9c1\uad00\uc744 \ucd94\uc0c1\uc801\uc778 \uacf5\ub9ac\ub85c \ud45c\ud604\ud55c \uad6c\uc870\ub2e4.<\/li>\n<\/ul>\n<p>\ubd80\ub974\ubc14\ud0a4\uc758 \uc5d0\uc138\uc774\ub294 \ub458 \uc774\uc0c1\uc758 \ubaa8\uad6c\uc870\uac00 \ub2e8\uc21c\ud788 \ub098\ub780\ud788 \ub193\uc774\ub294 \uac83\uc774 \uc544\ub2c8\ub77c \uadf8 \uc0ac\uc774\uc758 \uc591\ub9bd \uc870\uac74\uc744 \ub098\ud0c0\ub0b4\ub294 \uacf5\ub9ac\ub85c \uacb0\ud569\ub420 \ub54c <span class=\"defined\">\ub2e4\uc911 \uad6c\uc870<\/span>(multiple structure)\uac00 \uc0dd\uae34\ub2e4\uace0 \uc124\uba85\ud588\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \uc704\uc0c1 \ubca1\ud130\uacf5\uac04\uc740 \ubca1\ud130 \ub367\uc148\uacfc \uc2a4\uce7c\ub77c\ubc30\ub77c\ub294 \ub300\uc218\uc801 \uad6c\uc870\uc640 \uc704\uc0c1 \uad6c\uc870\ub97c \uac16\ub294 \ub370 \uadf8\uce58\uc9c0 \uc54a\uace0, \ub367\uc148\uacfc \uc2a4\uce7c\ub77c\ubc30\uac00 \uc5f0\uc18d\uc774\ub77c\ub294 \uc591\ub9bd \uc870\uac74\uc744 \ub9cc\uc871\ud574\uc57c \ud55c\ub2e4. <!-- \uc774 \ub3c4\uc2dd\uc740 \uc11c\ub85c \ub2e4\ub978 \ubd84\uc57c\uc758 \ub300\uc0c1\ub4e4\uc744 \ube44\uad50\ud558\ub294 \uc720\uc775\ud55c \uc9c0\ub3c4\uc600\uc9c0\ub9cc, \ubaa8\ub4e0 \uc218\ud559\uc774 \uc815\ud655\ud788 \uc138 \ubaa8\uad6c\uc870\uc758 \uc870\ud569\uc73c\ub85c \uc644\uc804\ud788 \ud658\uc6d0\ub41c\ub2e4\ub294 \uc815\ub9ac\ub3c4 \uc544\ub2c8\uace0 \ubd80\ub974\ubc14\ud0a4 \ucd1d\uc11c\uc5d0\uc11c \uc77c\uad00\ub418\uac8c \uc0ac\uc6a9\ub41c \ud615\uc2dd\uc801 \ubd84\ub958\ud45c\ub3c4 \uc544\ub2c8\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Bourbaki, N. (1950). \u201cThe Architecture of Mathematics.\u201d The American Mathematical Monthly, 57(4), 221\u2013232.\" href=\"#ref-Bourbaki1950\">[Bourbaki1950]<\/a><a class=\"math-abs-series-ref\" title=\"Corry, L. (1992). \u201cNicolas Bourbaki and the Concept of Mathematical Structure.\u201d Synthese, 92, 315\u2013348.\" href=\"#ref-Corry1992\">[Corry1992]<\/a> --><\/p>\n<p>\ubd80\ub974\ubc14\ud0a4\uc758 \ud615\uc2dd\uc801 \uccb4\uacc4\ub294 \uae30\ubcf8\uc801\uc73c\ub85c \uc9d1\ud569\uacfc \uc9d1\ud569 \uc704\uc5d0 \uc5b9\ud78c \uad6c\uc870\ub97c \ucd9c\ubc1c\uc810\uc73c\ub85c \uc0bc\uc558\ub2e4. <!-- \ub2e4\ub9cc \ubd80\ub974\ubc14\ud0a4\uac00 \uad6c\uc870 \ubcf4\uc874 \uc0ac\uc0c1\uc744 \ub2e8\uc21c\ud55c \ubd80\ucc28\uc801 \ub3c4\uad6c\ub85c\ub9cc \ucde8\uae09\ud588\ub2e4\uace0 \ub9d0\ud558\ub294 \uac83\ub3c4 \uc9c0\ub098\uce58\ub2e4. --> \uc900\ub3d9\ud615\uc0ac\uc0c1, \uc5f0\uc18d\ud568\uc218, \ub3d9\ud615\uc0ac\uc0c1\uc740 \ubd80\ub974\ubc14\ud0a4\uc758 \uc2e4\uc81c \uc218\ud559 \uc804\uac1c\uc5d0\uc11c\ub3c4 \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud588\ub2e4. \ucc28\uc774\ub294 \uadf8\ub7ec\ud55c \uc0ac\uc0c1\ub4e4\uc744 \ubc94\uc8fc\uc640 \ud568\uc790\ub77c\ub294 \uc77c\ubc18\uc801\uc778 \uc870\uc9c1 \uc6d0\ub9ac\ub85c \ucd1d\uc11c\uc758 \uae30\ucd08\uc5d0 \ud1b5\ud569\ud558\uc9c0 \uc54a\uc558\ub2e4\ub294 \ub370 \uc788\ub2e4.<a class=\"math-abs-series-ref\" title=\"Corry, L. (1992). \u201cNicolas Bourbaki and the Concept of Mathematical Structure.\u201d Synthese, 92, 315\u2013348.\" href=\"#ref-Corry1992\">[Corry1992]<\/a><\/p>\n<p>[\ubd80\ub974\ubc14\ud0a4\uac00 \ubc94\uc8fc\ub860\uc744 \uc54c\uc9c0 \ubabb\ud574 \ub2e8\uc21c\ud788 \u2018\uc678\uba74\ud588\ub2e4\u2019\ub294 \uc124\uba85\uc740 \uc815\ud655\ud558\uc9c0 \uc54a\ub2e4. \uc544\uc77c\ub80c\ubca0\ub974\ud06c\uc640 \uadf8\ub85c\ud150\ub514\ud06c \uac19\uc740 \ubc94\uc8fc\ub860 \uc5f0\uad6c\uc790\ub4e4\uc774 \ubd80\ub974\ubc14\ud0a4\uc5d0 \ucc38\uc5ec\ud588\uace0, \ub0b4\ubd80\uc5d0\uc11c\ub294 \ubc94\uc8fc\uc640 \ud638\ubab0\ub85c\uc9c0 \ub300\uc218\uc5d0 \uad00\ud55c \uc7a5\uc744 \ucd1d\uc11c\uc5d0 \ub123\ub294 \ubc29\uc548\ub3c4 \ub17c\uc758\ub418\uc5c8\uc9c0\ub9cc \ucd9c\ud310\ub41c \uae30\ucd08 \uccb4\uacc4\uc758 \uc911\uc2ec\uc5d0\ub294 \uc815\ucc29\ud558\uc9c0 \ubabb\ud588\ub2e4. <!-- \ub530\ub77c\uc11c \uc774 \uad00\uacc4\ub294 \ubb34\uc9c0\ub098 \ub2e8\uc21c\ud55c \uac70\ubd80\ub77c\uae30\ubcf4\ub2e4, \uc774\ubbf8 \uc9d1\ud569\uacfc \uad6c\uc870\uc5d0 \ub9de\ucd94\uc5b4 \uc791\uc131\ub41c \ucd1d\uc11c\uc640 \uc0c8 \ubc94\uc8fc\ub860\uc801 \uc5b8\uc5b4 \uc0ac\uc774\uc758 \uae34\uc7a5\uc73c\ub85c \ubcf4\ub294 \ud3b8\uc774 \uc815\ud655\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Corry, L. (1992). \u201cNicolas Bourbaki and the Concept of Mathematical Structure.\u201d Synthese, 92, 315\u2013348.\" href=\"#ref-Corry1992\">[Corry1992]<\/a>] --><\/p>\n<h4>\ubc94\uc8fc\ub860, \ub300\uc0c1\uacfc \uc0ac\uc0c1\uc744 \ud568\uaed8 \ubcf4\ub2e4<\/h4>\n<p>1945\ub144 \uc0c8\ubba4\uc5bc \uc544\uc77c\ub80c\ubca0\ub974\ud06c(Samuel Eilenberg)\uc640 \uc190\ub354\uc2a4 \ub9e4\ud074\ub808\uc778(Saunders Mac Lane)\uc740 \u201c\uc790\uc5f0\uc801 \ub3d9\uce58\uc758 \uc77c\ubc18 \uc774\ub860\u201d(<i>General Theory of Natural Equivalences<\/i>)\uc744 \ubc1c\ud45c\ud588\ub2e4. \uc6d0\ubb38\uc758 \uc81c\ubaa9\uc740 \u2018\uc790\uc5f0 \ubcc0\ud658\u2019\uc774 \uc544\ub2c8\ub77c \u2018\uc790\uc5f0\uc801 \ub3d9\uce58\u2019\ub2e4. \uc774\ub4e4\uc740 \ubca1\ud130\uacf5\uac04\uacfc \uadf8 \uc774\uc911\uc30d\ub300 \uc0ac\uc774\uc758 \ub300\uc751, \uc704\uc0c1\uc218\ud559\uc758 \ud638\ubab0\ub85c\uc9c0\uc640 \ucf54\ud638\ubab0\ub85c\uc9c0, \uadf9\ud55c\uc744 \ucde8\ud560 \ub54c \ubcf4\uc874\ub418\ub294 \ub3d9\ud615\uc0ac\uc0c1 \ub4f1 \uc5ec\ub7ec \ubd84\uc57c\uc5d0\uc11c \ub098\ud0c0\ub098\ub294 \u2018\uc790\uc5f0\uc131\u2019\uc744 \uc5c4\ubc00\ud558\uac8c \ub2e4\ub8e8\uace0\uc790 \ud588\ub2e4. \uc774\ub97c \uc704\ud574 \ubc94\uc8fc, \ud568\uc790, \uc790\uc5f0\uc801 \ub3d9\uce58\uc640 \uc790\uc5f0 \ubcc0\ud658\uc758 \uac1c\ub150\uc744 \ud558\ub098\uc758 \uc77c\ubc18 \uc774\ub860 \uc548\uc5d0\uc11c \uccb4\uacc4\ud654\ud588\ub2e4. <!-- \uc774 \uac1c\ub150\ub4e4\uc758 \uc608\ube44 \ud615\ud0dc\ub294 \ub450 \uc800\uc790\uac00 1942\ub144\uc5d0 \ubc1c\ud45c\ud55c \uad70\ub860 \ub17c\ubb38\uc5d0\ub3c4 \uc774\ubbf8 \ub4f1\uc7a5\ud558\ubbc0\ub85c, \ubc94\uc8fc\ub860\uc774 1945\ub144 \ud55c \ub17c\ubb38\uc758 \ubcf4\uc870 \uc815\uc758\uc5d0\uc11c \uc6b0\uc5f0\ud788 \uc0dd\uaca8\ub0ac\ub2e4\uace0\ub9cc \uc124\uba85\ud558\ub294 \uac83\ub3c4 \ub2e8\uc21c\ud654\ub2e4.<a class=\"math-abs-series-ref\" title=\"Eilenberg, S., &amp; Mac Lane, S. (1945). \u201cGeneral Theory of Natural Equivalences.\u201d Transactions of the American Mathematical Society, 58(2), 231\u2013294.\" href=\"#ref-EilenbergMacLane1945\">[EilenbergMacLane1945]<\/a> --><\/p>\n<p>\uc774 \uae00\uc5d0\uc11c\ub294 \ud06c\uae30 \ubb38\uc81c\ub97c \ud53c\ud558\uae30 \uc704\ud574 <span class=\"defined\">\uad6d\uc18c\uc801\uc73c\ub85c \uc791\uc740 \ubc94\uc8fc<\/span>(locally small category)\ub9cc\uc744 \uc0dd\uac01\ud558\uc790. \uadf8\ub7ec\ud55c \ubc94\uc8fc \\(\\mathcal C\\)\ub294 \ub2e4\uc74c \uc790\ub8cc\uc640 \ubc95\uce59\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><a class=\"math-abs-series-ref\" title=\"Mac Lane, S. (1998). Categories for the Working Mathematician (2nd ed.). Springer.\" href=\"#ref-MacLane1998\">[MacLane1998]<\/a><\/p>\n<ul>\n<li>\ub300\uc0c1(object)\ub4e4\uc758 \ubaa8\uc784\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/li>\n<li>\uac01 \ub450 \ub300\uc0c1 \\(A,B\\)\uc5d0 \ub300\ud558\uc5ec \\(A\\)\uc5d0\uc11c \\(B\\)\ub85c \uac00\ub294 <span class=\"defined\">\uc0ac\uc0c1<\/span>(morphism)\ub4e4\uc758 \uc9d1\ud569 \\(\\operatorname{Hom}_{\\mathcal C}(A,B)\\)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/li>\n<li>\uac01 \uc138 \ub300\uc0c1 \\(A,B,C\\)\uc5d0 \ub300\ud558\uc5ec \uc0ac\uc0c1\uc758 \ud569\uc131<br \/>\n    \\[<br \/>\n    \\operatorname{Hom}_{\\mathcal C}(B,C)\\times\\operatorname{Hom}_{\\mathcal C}(A,B)<br \/>\n    \\longrightarrow \\operatorname{Hom}_{\\mathcal C}(A,C),\\qquad (g,f)\\longmapsto g\\circ f<br \/>\n    \\]<br \/>\n    \uc774 \uc8fc\uc5b4\uc9c0\uace0, \ud569\uc131\uc740 \uacb0\ud569\ubc95\uce59 \\((h\\circ g)\\circ f=h\\circ(g\\circ f)\\)\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/li>\n<li>\uac01 \ub300\uc0c1 \\(A\\)\uc5d0\ub294 \ud56d\ub4f1\uc0ac\uc0c1 \\(\\operatorname{id}_A:A\\to A\\)\uac00 \uc788\uc5b4, \ubaa8\ub4e0 \\(f:A\\to B\\)\uc5d0 \ub300\ud574<br \/>\n    \\[<br \/>\n    f\\circ\\operatorname{id}_A=f=\\operatorname{id}_B\\circ f<br \/>\n    \\]<br \/>\n    \uac00 \uc131\ub9bd\ud55c\ub2e4.<\/li>\n<\/ul>\n<p>\uc9d1\ud569\uc744 \ub300\uc0c1\uc73c\ub85c \ud558\uace0 \ud568\uc218\ub97c \uc0ac\uc0c1\uc73c\ub85c \ud558\ub294 \\(\\mathrm{Set}\\), \uad70\uc744 \ub300\uc0c1\uc73c\ub85c \ud558\uace0 \uad70 \uc900\ub3d9\ud615\uc0ac\uc0c1\uc744 \uc0ac\uc0c1\uc73c\ub85c \ud558\ub294 \\(\\mathrm{Grp}\\)\uac00 \ub300\ud45c\uc801\uc778 \uc608\ub2e4. \ud1b5\uc0c1\uc801\uc778 \uc9d1\ud569\ub860\uc801 \uae30\ucd08\uc5d0\uc11c \\(\\mathrm{Set}\\)\uacfc \\(\\mathrm{Grp}\\)\uc758 \ub300\uc0c1 \uc804\uccb4\ub294 \ud558\ub098\uc758 \uc9d1\ud569\uc774 \uc544\ub2c8\ubbc0\ub85c \uc774\ub4e4\uc740 <span class=\"defined\">\ud070 \ubc94\uc8fc<\/span>(large category)\ub2e4. \uadf8\ub7ec\ub098 \ub450 \uace0\uc815\ub41c \ub300\uc0c1 \uc0ac\uc774\uc758 \uc0ac\uc0c1\ub4e4\uc740 \uc9d1\ud569\uc744 \uc774\ub8e8\ubbc0\ub85c \uad6d\uc18c\uc801\uc73c\ub85c \uc791\ub2e4. \uc2e4\uc81c \uc791\uc5c5\uc5d0\uc11c\ub294 \uc6b0\uc8fc(universe) \uac19\uc740 \ud06c\uae30 \uad00\ub840\ub97c \ucc44\ud0dd\ud558\uae30\ub3c4 \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><\/p>\n<p>\ubc94\uc8fc\ub860\uc758 \ubcc0\ud654\ub294 \ub300\uc0c1\uc744 \uc5c6\uc560\uace0 \uc0ac\uc0c1\ub9cc \ub0a8\uae34 \ub370 \uc788\uc9c0 \uc54a\ub2e4. \uc544\uc77c\ub80c\ubca0\ub974\ud06c\uc640 \ub9e4\ud074\ub808\uc778\uc740 \uc624\ud788\ub824 \u2018\ub300\uc0c1\uacfc \uadf8 \uc0ac\uc0c1\uc744 \ub3d9\uc2dc\uc5d0 \uace0\ub824\u2019\ud574\uc57c \ud55c\ub2e4\uace0 \uac15\uc870\ud588\ub2e4. \ubc94\uc8fc\ub860\uc740 \ub300\uc0c1\uc758 \ub0b4\ubd80 \uc6d0\uc18c\ub97c \ub9e4\ubc88 \uc9c1\uc811 \uc5b8\uae09\ud558\uc9c0 \uc54a\uace0 \ud569\uc131\u00b7\ud56d\ub4f1\uc0ac\uc0c1\u00b7\uac00\ud658\ub3c4\uc2dd\u00b7\ubcf4\ud3b8 \uc131\uc9c8\ub85c \ub9ce\uc740 \ub17c\uc99d\uc744 \uc804\uac1c\ud560 \uc218 \uc788\uac8c \ud558\uc9c0\ub9cc, \ub300\uc0c1\uacfc \uc0ac\uc0c1\uc758 \uc815\uc758\uc5ed\u00b7\uacf5\uc5ed\uc740 \uc5ec\uc804\ud788 \ud544\uc218\ub2e4. \ub610\ud55c \\(\\mathrm{Set}\\), \\(\\mathrm{Grp}\\), \uc704\uc0c1\uacf5\uac04\uc758 \ubc94\uc8fc \uac19\uc740 \uad6c\uccb4\uc801 \ubc94\uc8fc\uc5d0\uc11c\ub294 \uc6d0\uc18c\ub97c \uc774\uc6a9\ud55c \ub17c\uc99d\ub3c4 \uacc4\uc18d \uc720\ud6a8\ud558\ub2e4. <!-- \ub530\ub77c\uc11c \ubc94\uc8fc\ub860\uc744 \u2018\ub0b4\ubd80\ub97c \uc77c\uc808 \ubcf4\uc9c0 \uc54a\ub294 \ucd08\uc6d4\uc801 \uc774\ub860\u2019\uc774\ub77c\uace0 \ud558\uae30\ubcf4\ub2e4, \ub300\uc0c1\uacfc \uc0ac\uc0c1\uc744 \ud568\uaed8 \ub193\uace0 \uc11c\ub85c \ub2e4\ub978 \ubd84\uc57c\uc758 \uad6c\uc131\uc744 \ube44\uad50\ud558\ub294 \uc5b8\uc5b4\ub77c\uace0 \uc124\uba85\ud558\ub294 \ud3b8\uc774 \uc815\ud655\ud558\ub2e4. <a class=\"math-abs-series-ref\" title=\"Eilenberg, S., &amp; Mac Lane, S. (1945). \u201cGeneral Theory of Natural Equivalences.\u201d Transactions of the American Mathematical Society, 58(2), 231\u2013294.\" href=\"#ref-EilenbergMacLane1945\">[EilenbergMacLane1945]<\/a><a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a> --> \uacb0\uad6d \ubc94\uc8fc\ub860\uc740 \ub300\uc0c1\uacfc \uc0ac\uc0c1\uc744 \ud568\uaed8 \ub193\uace0 \uc11c\ub85c \ub2e4\ub978 \ubd84\uc57c\uc758 \uad6c\uc131\uc744 \ube44\uad50\ud558\ub294 \uc5b8\uc5b4\uc774\ub2e4.<\/p>\n<p>[\u2018\ucd94\uc0c1\uc801 \ud5db\uc18c\ub9ac\u2019 \ub610\ub294 \u2018\uc77c\ubc18 \ucd94\uc0c1\uc801 \ud5db\uc18c\ub9ac\u2019(abstract nonsense, general abstract nonsense)\ub294 \ubc94\uc8fc\ub860\uc801\uc774\uace0 \ud615\uc2dd\uc801\uc778 \uc77c\ubc18 \ub17c\uc99d\uc744 \uac00\ub9ac\ud0a4\ub294 \uc790\uc870\uc801 \ud45c\ud604\uc73c\ub85c \uc815\ucc29\ud588\ub2e4. \ub9e4\ud074\ub808\uc778\uc740 1997\ub144 \ud68c\uace0\uc5d0\uc11c \ubc94\uc8fc\uc758 \ub9e4\uc6b0 \ucd94\uc0c1\uc801\uc778 \uc544\uc774\ub514\uc5b4\uac00 \ub2f9\uc2dc \u201cgeneral abstract nonsense\u201d\ub77c\uace0 \ubd88\ub838\ub2e4\uace0 \uc37c\ub2e4.<!-- \ub2e4\ub9cc \uc774 \uc790\ub8cc\ub9cc\uc73c\ub85c \ucd08\ucc3d\uae30 \ubc94\uc8fc\ub860 \ud559\uc790\ub4e4 \ubaa8\ub450\uac00 \uc6d0\uc18c \uc5c6\ub294 \uc99d\uba85\uc744 \uc2a4\uc2a4\ub85c \uc870\ub871\ud558\uba70 \uac19\uc740 \uc774\ub984\uc744 \ubd99\uc600\ub2e4\uace0 \ub2e8\uc815\ud560 \uc218 \uc5c6\uace0, \ub178\uba3c \uc2a4\ud2f4\ub85c\ub4dc\uac00 \ud45c\ud604\uc744 \ub9cc\ub4e4\uc5c8\ub2e4\ub294 \ud754\ud55c \uadc0\uc18d\ub3c4 \ud655\uc815\ub41c 1\ucc28 \uae30\ub85d\uc774 \ubd80\uc871\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Mac Lane, S. (1997). \u201cThe PNAS Way Back Then.\u201d Proceedings of the National Academy of Sciences, 94(12), 5983\u20135985.\" href=\"#ref-MacLane1997\">[MacLane1997]<\/a> -->]<\/p>\n<p>\uc774 \uc0ac\uc0c1 \uc911\uc2ec\uc758 \uc11c\uc220 \ubc29\uc2dd\uc774 \uc2e4\uc804\uc5d0\uc11c \uc5b4\ub5bb\uac8c \uc791\ub3d9\ud558\ub294\uc9c0 \uacf1\uc758 \uc815\uc758\ub97c \ud1b5\ud574 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n<h4>\uacf1\uc758 \ubcf4\ud3b8 \uc131\uc9c8<\/h4>\n<p>\ub450 \uc9d1\ud569 \\(A\\)\uc640 \\(B\\)\uc758 \uacf1\uc9d1\ud569(cartesian product)\uc740 \ubcf4\ud1b5<br \/>\n\\[<br \/>\nA\\times B=\\{(a,b):a\\in A,\\ b\\in B\\}<br \/>\n\\]<br \/>\n\ub85c \uc815\uc758\ud55c\ub2e4. \uadf8\ub7ec\ub098 \ub9ce\uc740 \ub17c\uc99d\uc5d0\uc11c \uc911\uc694\ud55c \uac83\uc740 \uc21c\uc11c\uc30d\uc758 \uad6c\uccb4\uc801\uc778 \uc9d1\ud569\ub860\uc801 \uad6c\ud604\uc774 \uc544\ub2c8\ub77c \ub450 \uc0ac\uc601\ud568\uc218 \\(\\pi_A:A\\times B\\to A\\), \\(\\pi_B:A\\times B\\to B\\)\uac00 \ub9cc\uc871\ud558\ub294 \uc131\uc9c8\uc774\ub2e4. \uc784\uc758\uc758 \uc9d1\ud569 \\(X\\)\uc640 \ub450 \ud568\uc218 \\(f:X\\to A\\), \\(g:X\\to B\\)\uac00 \uc8fc\uc5b4\uc9c8 \ub54c<br \/>\n\\[<br \/>\nh(x)=(f(x),g(x))<br \/>\n\\]<br \/>\n\ub85c \uc815\uc758\ub418\ub294 \ud568\uc218 \\(h:X\\to A\\times B\\)\uac00 \uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud558\uc5ec<br \/>\n\\[<br \/>\n\\pi_A\\circ h=f,\\qquad \\pi_B\\circ h=g<br \/>\n\\]<br \/>\n\ub97c \ub9cc\uc871\ud55c\ub2e4. \uc774 \uc131\uc9c8\uc740 \uc21c\uc11c\uc30d\uc744 \uc5b8\uae09\ud558\uc9c0 \uc54a\uace0\ub3c4 \uc784\uc758\uc758 \ubc94\uc8fc\uc5d0\uc11c \uacf1\uc744 \uc815\uc758\ud560 \uc218 \uc788\uac8c \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><a class=\"math-abs-series-ref\" title=\"Mac Lane, S. (1998). Categories for the Working Mathematician (2nd ed.). Springer.\" href=\"#ref-MacLane1998\">[MacLane1998]<\/a><\/p>\n<div class=\"box theorem\">\n<p>\n<span class=\"theorem\">\uacf1\uc758 \ubcf4\ud3b8 \uc131\uc9c8<\/span>(Universal Property of Product)<br \/>\n\ubc94\uc8fc \\(\\mathcal C\\)\uc758 \ub450 \ub300\uc0c1 \\(A,B\\)\uac00 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \ub300\uc0c1 \\(P\\)\uc640 \ub450 \uc0ac\uc0c1<br \/>\n\\[<br \/>\n\\pi_A:P\\to A,\\qquad \\pi_B:P\\to B<br \/>\n\\]<br \/>\n\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc0bc\uc911\ud56d \\((P,\\pi_A,\\pi_B)\\)\uac00 \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud558\uba74 \uc774\ub97c \\(A\\)\uc640 \\(B\\)\uc758 <span class=\"defined\">\uacf1<\/span>(product)\uc774\ub77c\uace0 \ud55c\ub2e4.<\/p>\n<p>\uc784\uc758\uc758 \ub300\uc0c1 \\(X\\)\uc640 \uc784\uc758\uc758 \ub450 \uc0ac\uc0c1 \\(f:X\\to A\\), \\(g:X\\to B\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\n\\pi_A\\circ h=f,\\qquad \\pi_B\\circ h=g<br \/>\n\\]<br \/>\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc0ac\uc0c1 \\(h:X\\to P\\)\uac00 \uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<p>\uc774 \uc0ac\uc0c1\uc744 \ud754\ud788 \\(h=\\langle f,g\\rangle\\)\ub85c \uc4f4\ub2e4. \uacf1\uc774 \uc874\uc7ac\ud560 \ub54c \ub300\uc0c1 \ubd80\ubd84\uc744 \\(A\\times B\\)\ub77c\uace0 \ud45c\uae30\ud55c\ub2e4. \ubaa8\ub4e0 \ubc94\uc8fc\uc5d0 \ubaa8\ub4e0 \ub450 \ub300\uc0c1\uc758 \uacf1\uc774 \uc874\uc7ac\ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4.<\/p>\n<\/div>\n<p>\uc774\ucc98\ub7fc \uc5b4\ub5a4 \ub300\uc0c1\uc744 \ub0b4\ubd80 \uc6d0\uc18c\uc758 \ud2b9\uc815 \uad6c\ud604\uc774 \uc544\ub2c8\ub77c \uc678\ubd80 \ub300\uc0c1\uc5d0\uc11c \ub4e4\uc5b4\uc624\ub294 \ubaa8\ub4e0 \uc0ac\uc0c1\uc5d0 \ub300\ud574 \ub9cc\uc871\ud558\ub294 \uc874\uc7ac\uc131\uacfc \uc720\uc77c\uc131 \uc870\uac74\uc73c\ub85c \uaddc\uc815\ud558\ub294 \uac83\uc774 <span class=\"defined\">\ubcf4\ud3b8 \uc131\uc9c8<\/span>(universal property)\uc744 \uc0ac\uc6a9\ud55c \uc815\uc758\uc758 \ud55c \uc804\ud615\uc774\ub2e4. \uacf1\uc758 \uacbd\uc6b0\uc5d0\ub294 \\(P\\)\ub85c \ub4e4\uc5b4\uc624\ub294 \uc0ac\uc0c1\ub4e4\uc774 \ub450 \uc131\ubd84 \uc0ac\uc0c1\uacfc \uc815\ud655\ud788 \ub300\uc751\ud55c\ub2e4\ub294 \uc810\uc774 \ud575\uc2ec\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><a class=\"math-abs-series-ref\" title=\"Mac Lane, S. (1998). Categories for the Working Mathematician (2nd ed.). Springer.\" href=\"#ref-MacLane1998\">[MacLane1998]<\/a><\/p>\n<div class=\"box theorem\">\n<p>\n<span class=\"theorem\">\uc815\ub9ac: \uacf1\uc758 \ub3d9\ud615\uae4c\uc9c0\uc758 \uc720\uc77c\uc131<\/span><br \/>\n\ub3d9\uc77c\ud55c \ub450 \ub300\uc0c1 \\(A,B\\)\uc5d0 \ub300\ud558\uc5ec \\((P,\\pi_A,\\pi_B)\\)\uc640 \\((P&#8217;,\\pi_A&#8217;,\\pi_B&#8217;)\\)\uac00 \ubaa8\ub450 \uacf1\uc774\ub77c \ud558\uc790. \uadf8\ub7ec\uba74<br \/>\n\\[<br \/>\n\\pi_A&#8217;\\circ\\varphi=\\pi_A,\\qquad \\pi_B&#8217;\\circ\\varphi=\\pi_B<br \/>\n\\]<br \/>\n\ub97c \ub9cc\uc871\ud558\ub294 \ub3d9\ud615\uc0ac\uc0c1 \\(\\varphi:P\\to P&#8217;\\)\uac00 \uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud55c\ub2e4.<\/p>\n<\/div>\n<p>\uc99d\uba85\uc740 \ubcf4\ud3b8 \uc131\uc9c8\uc744 \ub450 \ubc88 \uc801\uc6a9\ud558\uba74 \ub41c\ub2e4. \\(P&#8217;\\)\uc758 \ubcf4\ud3b8 \uc131\uc9c8\uc5d0\uc11c \uc2dc\ud5d8 \ub300\uc0c1 \\(X=P\\), \ub450 \uc0ac\uc0c1 \\(f=\\pi_A\\), \\(g=\\pi_B\\)\ub97c \ud0dd\ud558\uba74<br \/>\n\\[<br \/>\n\\pi_A&#8217;\\circ\\varphi=\\pi_A,\\qquad \\pi_B&#8217;\\circ\\varphi=\\pi_B<br \/>\n\\]<br \/>\n\ub97c \ub9cc\uc871\ud558\ub294 \uc720\uc77c\ud55c \uc0ac\uc0c1 \\(\\varphi:P\\to P&#8217;\\)\ub97c \uc5bb\ub294\ub2e4. \ubc18\ub300\ub85c \\(P\\)\uc758 \ubcf4\ud3b8 \uc131\uc9c8\uc5d0 \\(X=P&#8217;\\), \\(f=\\pi_A&#8217;\\), \\(g=\\pi_B&#8217;\\)\ub97c \ub123\uc73c\uba74<br \/>\n\\[<br \/>\n\\pi_A\\circ\\psi=\\pi_A&#8217;,\\qquad \\pi_B\\circ\\psi=\\pi_B&#8217;<br \/>\n\\]<br \/>\n\ub97c \ub9cc\uc871\ud558\ub294 \uc720\uc77c\ud55c \uc0ac\uc0c1 \\(\\psi:P&#8217;\\to P\\)\ub97c \uc5bb\ub294\ub2e4.<\/p>\n<p>\uc774\uc81c \\(\\psi\\circ\\varphi:P\\to P\\)\uc5d0 \ub450 \uc0ac\uc601\uc744 \ud569\uc131\ud558\uba74<br \/>\n\\[\\begin{aligned}<br \/>\n\\pi_A\\circ(\\psi\\circ\\varphi)<br \/>\n&#038;=(\\pi_A\\circ\\psi)\\circ\\varphi<br \/>\n=\\pi_A&#8217;\\circ\\varphi<br \/>\n=\\pi_A,\\\\<br \/>\n\\pi_B\\circ(\\psi\\circ\\varphi)<br \/>\n&#038;=(\\pi_B\\circ\\psi)\\circ\\varphi<br \/>\n=\\pi_B&#8217;\\circ\\varphi<br \/>\n=\\pi_B.<br \/>\n\\end{aligned}\\]<br \/>\n\\(\\operatorname{id}_P\\)\ub3c4 \ub611\uac19\uc740 \ub450 \ub4f1\uc2dd\uc744 \ub9cc\uc871\ud55c\ub2e4. \uadf8\ub7f0\ub370 \\(P\\)\uc758 \ubcf4\ud3b8 \uc131\uc9c8\uc740 \uc774 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \\(P\\to P\\) \uc0ac\uc0c1\uc774 \uc720\uc77c\ud558\ub2e4\uace0 \ub9d0\ud558\ubbc0\ub85c<br \/>\n\\[<br \/>\n\\psi\\circ\\varphi=\\operatorname{id}_P<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ub300\uce6d\uc801\uc73c\ub85c<br \/>\n\\[<br \/>\n\\varphi\\circ\\psi=\\operatorname{id}_{P&#8217;}<br \/>\n\\]<br \/>\n\ub3c4 \uc5bb\ub294\ub2e4. \ub530\ub77c\uc11c \\(\\varphi\\)\uc640 \\(\\psi\\)\ub294 \uc11c\ub85c \uc5ed\uc778 \uc0ac\uc0c1\uc774\uace0 \\(\\varphi\\)\ub294 \ub3d9\ud615\uc0ac\uc0c1\uc774\ub2e4. \ucc98\uc74c \ubcf4\ud3b8 \uc131\uc9c8\uc744 \uc801\uc6a9\ud560 \ub54c\ubd80\ud130 \ub450 \uc0ac\uc601\uacfc \uc591\ub9bd\ud558\ub294 \\(\\varphi\\)\ub294 \uc720\uc77c\ud588\uc73c\ubbc0\ub85c \uc815\ub9ac\uac00 \uc99d\uba85\ub418\uc5c8\ub2e4.<span class=\"qed\"><\/span><\/p>\n<p>\uc5ec\uae30\uc11c \uc720\uc77c\ud558\ub2e4\ub294 \uac83\uc740 \\(P\\)\uc640 \\(P&#8217;\\) \uc0ac\uc774\uc758 \ubaa8\ub4e0 \ub3d9\ud615\uc0ac\uc0c1 \uac00\uc6b4\ub370 \ud558\ub098\ub9cc \uc874\uc7ac\ud55c\ub2e4\ub294 \ub73b\uc774 \uc544\ub2c8\ub2e4. \ub450 \uc0ac\uc601\uacfc \uc591\ub9bd\ud558\ub294 \ub3d9\ud615\uc0ac\uc0c1\uc774 \uc720\uc77c\ud558\ub2e4\ub294 \ub73b\uc774\ub2e4. <!-- \ub610\ud55c \u201c\ub3d9\ud615\uae4c\uc9c0 \uc720\uc77c\ud558\ub2e4\u201d\ub294 \ub9d0\uc740 \uacf1\uc758 \uc5ec\ub7ec \uad6c\uccb4\uc801 \uad6c\ud604\uc744 \ubb38\uc790 \uadf8\ub300\ub85c \uac19\uc740 \uc9d1\ud569\uc774\ub098 \uac19\uc740 \ub300\uc0c1\uc73c\ub85c \ub9cc\ub4e4\uc9c0 \uc54a\ub294\ub2e4. --> \ub2e4\ub9cc \ubc94\uc8fc\uc5d0\uc11c \uacf1\uc73c\ub85c\uc11c \uc218\ud589\ud558\ub294 \uc5ed\ud560\uc740 \uc720\uc77c\ud55c \ud638\ud658 \ub3d9\ud615\uc0ac\uc0c1\uc744 \ud1b5\ud574 \uac19\uc544\uc9c4\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><\/p>\n<p>\ubcf4\ud3b8 \uc131\uc9c8\uc740 \uacf1\uc5d0\ub9cc \uc4f0\uc774\uc9c0 \uc54a\ub294\ub2e4. \ubaab\uad70\uacfc \ubaab\ubca1\ud130\uacf5\uac04\uc740 \ud2b9\uc815 \uc0ac\uc0c1\ub4e4\uc744 \uac19\uac8c \ub9cc\ub4e4\uac70\ub098 \uc8fc\uc5b4\uc9c4 \ubd80\ubd84\ub300\uc0c1\uc744 0\uc73c\ub85c \ubcf4\ub0b4\ub294 \uc0ac\uc0c1\ub4e4\uc774 \uc720\uc77c\ud558\uac8c \uc778\uc218\ubd84\ud574\ub418\ub294 \uc131\uc9c8\ub85c \uc124\uba85\ud560 \uc218 \uc788\ub2e4. \uc790\uc720\uad70\uc740 \uc9d1\ud569\uc5d0\uc11c \uad70\uc73c\ub85c \uac00\ub294 \uc790\uc720 \ud568\uc790\uc640 \ub9dd\uac01 \ud568\uc790\uc758 \uc218\ubc18 \uad00\uacc4\ub85c, \ud150\uc11c\uacf1\uc740 \uc30d\uc120\ud615 \uc0ac\uc0c1\ub4e4\uc744 \uc120\ud615 \uc0ac\uc0c1\uc73c\ub85c \ud45c\ud604\ud558\ub294 \ubcf4\ud3b8 \uc131\uc9c8\ub85c \ud2b9\uc9d5\uc9c0\uc5b4\uc9c4\ub2e4. \uc774\ub4e4\uc740 \ubaa8\ub450 \u2018\ubcf4\ud3b8\uc801\uc778 \uc0ac\uc0c1\u2019\uc744 \uc0ac\uc6a9\ud558\uc9c0\ub9cc \uacf1\uacfc \uc644\uc804\ud788 \uac19\uc740 \ubaa8\uc591\uc740 \uc544\ub2c8\ub2e4. \ubc94\uc8fc\ub860\uc740 \uc774 \uc5ec\ub7ec \ud328\ud134\uc744 \uadf9\ud55c\uacfc \uc30d\ub300\uadf9\ud55c, \ud45c\ud604\uac00\ub2a5\uc131, \uc218\ubc18 \ub4f1\uc758 \ub354 \ud070 \ud2c0\uc5d0\uc11c \ube44\uad50\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><a class=\"math-abs-series-ref\" title=\"Mac Lane, S. (1998). Categories for the Working Mathematician (2nd ed.). Springer.\" href=\"#ref-MacLane1998\">[MacLane1998]<\/a><\/p>\n<h4>\uc218\ub294 \uad6c\uc870\ub2e4<\/h4>\n<p>\ubcf4\ud3b8 \uc131\uc9c8\uc774 \uad6c\uccb4\uc801 \uad6c\ud604\uacfc \uadf8\uac83\uc774 \uc218\ud589\ud558\ub294 \ubc94\uc8fc\uc801 \uc5ed\ud560\uc744 \uad6c\ubcc4\ud558\uac8c \ud55c\ub2e4\ub294 \uad00\uc810\uc744, <a href=\"..\/math-abstraction-04-axiomatic-method\/\">4\ubd80<\/a>\uc5d0\uc11c \ub2e4\ub8e8\uc5c8\ub358 \uc9c8\ubb38\uc73c\ub85c \ub418\ub3cc\ub824 \ubcf4\uc790. \u201c\uc790\uc5f0\uc218\ub780 \ubb34\uc5c7\uc778\uac00?\u201d<\/p>\n<p>\uc624\ub298\ub0a0 \ud45c\uc900\uc801\uc778 \uc9d1\ud569\ub860\uc5d0\uc11c\ub294 \uc720\ud55c \ud3f0 \ub178\uc774\ub9cc \uc21c\uc11c\uc218(von Neumann ordinal)\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc790\uc5f0\uc218\ub97c<br \/>\n\\[<br \/>\n0=\\varnothing,\\quad<br \/>\n1=\\{0\\},\\quad<br \/>\n2=\\{0,1\\},\\quad<br \/>\n3=\\{0,1,2\\},\\quad\\ldots<br \/>\n\\]<br \/>\n\ub85c \uad6c\ud604\ud55c\ub2e4. \ud6c4\uc18d\uc790\ub294 \\(S(n)=n\\cup\\{n\\}\\)\uc774\ub2e4. \ud3f0 \ub178\uc774\ub9cc\uc740 1923\ub144 \ub17c\ubb38\uc5d0\uc11c \uac01 \uc21c\uc11c\uc218\ub97c \uadf8\ubcf4\ub2e4 \uc791\uc740 \ubaa8\ub4e0 \uc21c\uc11c\uc218\uc758 \uc9d1\ud569\uc73c\ub85c \ub098\ud0c0\ub0b4\ub294 \ubc29\uc2dd\uc73c\ub85c \uc720\ud55c \uc21c\uc11c\uc218\uc640 \ucd08\ud55c \uc21c\uc11c\uc218\ub97c \ud558\ub098\uc758 \uc9d1\ud569\ub860\uc801 \uccb4\uacc4 \uc548\uc5d0 \ub193\uc558\ub2e4.<a class=\"math-abs-series-ref\" title=\"von Neumann, J. (1923). \u201cZur Einf\u00fchrung der transfiniten Zahlen.\u201d Acta Scientiarum Mathematicarum (Szeged), 1(4), 199\u2013208.\" href=\"#ref-VonNeumann1923\">[VonNeumann1923]<\/a><a class=\"math-abs-series-ref\" title=\"Reck, E., &amp; Schiemer, G. (2021). \u201cStructuralism in the Philosophy of Mathematics.\u201d In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2021 ed.).\" href=\"#ref-ReckSchiemer2021\">[ReckSchiemer2021]<\/a><\/p>\n<p>\uc774\uc640 \ub300\uc870\ub418\ub294 \uad6c\ud604\uc73c\ub85c \ud754\ud788 <span class=\"defined\">\uc720\ud55c \uccb4\ub974\uba5c\ub85c \uc21c\uc11c\uc218<\/span>(finite Zermelo ordinals)\ub77c\uace0 \ubd80\ub974\ub294 \uc5f4\uc774 \uc788\ub2e4.<br \/>\n\\[<br \/>\n0_Z=\\varnothing,\\quad<br \/>\n1_Z=\\{\\varnothing\\},\\quad<br \/>\n2_Z=\\{\\{\\varnothing\\}\\},\\quad<br \/>\n3_Z=\\{\\{\\{\\varnothing\\}\\}\\},\\quad\\ldots<br \/>\n\\]<br \/>\n\uc5ec\uae30\uc11c\ub294 \ud6c4\uc18d\uc790\ub97c \\(S_Z(n)=\\{n\\}\\)\uc73c\ub85c \ub454\ub2e4. \uccb4\ub974\uba5c\ub85c\uc758 1908\ub144 \uc9d1\ud569\ub860 \uacf5\ub9ac\ud654\uc5d0\uc11c \ubb34\ud55c \uacf5\ub9ac\ub294 \uacf5\uc9d1\ud569\uc744 \uc6d0\uc18c\ub85c \ud3ec\ud568\ud558\uace0, \uc6d0\uc18c \\(a\\)\uc640 \ud568\uaed8 \ud55c\uc6d0\uc18c\uc9d1\ud569 \\(\\{a\\}\\)\ub3c4 \uc6d0\uc18c\ub85c \ud3ec\ud568\ud558\ub294 \uc9d1\ud569\uc758 \uc874\uc7ac\ub97c \uc694\uad6c\ud588\ub2e4. \uc774 \uacfc\uc815\uc744 \uc720\ud55c\ud558\uac8c \ubc18\ubcf5\ud574 \uc5bb\ub294 \uc704\uc758 \uc5f4\uc740 \ud6c4\ub300\uc5d0 \uc720\ud55c \uccb4\ub974\uba5c\ub85c \uc21c\uc11c\uc218 \ub610\ub294 \uccb4\ub974\uba5c\ub85c \uc218\ub77c\uace0 \ubd88\ub838\ub2e4. \uc5ec\uae30\uc11c\ub294 \uc5ed\uc0ac\uc801 \uc6b0\uc120\uad8c\ubcf4\ub2e4 \ubca0\ub098\uc138\ub77c\ud504\uac00 \uc0ac\uc6a9\ud55c \ub450 \uc9d1\ud569\ub860\uc801 \uad6c\ud604\uc758 \ub300\ube44\uc5d0 \ucd08\uc810\uc744 \ub9de\ucd94\uc790.<a class=\"math-abs-series-ref\" title=\"Zermelo, E. (1908). \u201cUntersuchungen \u00fcber die Grundlagen der Mengenlehre. I.\u201d Mathematische Annalen, 65, 261\u2013281.\" href=\"#ref-Zermelo1908\">[Zermelo1908]<\/a><a class=\"math-abs-series-ref\" title=\"Benacerraf, P. (1965). \u201cWhat Numbers Could Not Be.\u201d The Philosophical Review, 74(1), 47\u201373.\" href=\"#ref-Benacerraf1965\">[Benacerraf1965]<\/a><a class=\"math-abs-series-ref\" title=\"Reck, E., &amp; Schiemer, G. (2021). \u201cStructuralism in the Philosophy of Mathematics.\u201d In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2021 ed.).\" href=\"#ref-ReckSchiemer2021\">[ReckSchiemer2021]<\/a><\/p>\n<p>\uc801\uc808\ud55c \ud6c4\uc18d\ud568\uc218\uc640 \ub367\uc148\u00b7\uacf1\uc148\uc744 \uac01\uac01 \uc815\uc758\ud558\uba74 \ub450 \uccb4\uacc4\ub294 \uc790\uc5f0\uc218 \uad6c\uc870\ub85c\uc11c \ub3d9\ud615\uc774\uba70 \uac19\uc740 \uc0b0\uc220 \uba85\uc81c\ub4e4\uc744 \ub9cc\uc871\ud55c\ub2e4. <!-- \uc5ec\uae30\uc11c \u2018\ubaa8\uc21c \uc5c6\uc774 \ud398\uc544\ub178 \uacf5\ub9ac\ub97c \ub9cc\uc871\ud55c\ub2e4\u2019\ub294 \ud45c\ud604\uc740 \ubc30\uacbd \uc9d1\ud569\ub860\uacfc \ub3c5\ub9bd\ub41c \uc808\ub300\uc801 \ubb34\ubaa8\uc21c\uc131 \uc99d\uba85\uc744 \ub73b\ud558\uc9c0 \uc54a\ub294\ub2e4. --> \ubc30\uacbd \uc9d1\ud569\ub860 \uc548\uc5d0\uc11c \ub450 \uc5f4\uc740 \ud45c\uc900 \uc790\uc5f0\uc218 \uad6c\uc870\uc758 \ub450 \uad6c\ud604\uc744 \uc774\ub8ec\ub2e4. <!-- \uc774\ub294 1\ucc28 \ud398\uc544\ub178 \uc0b0\uc220\uc758 \ubaa8\ub4e0 \ubaa8\ud615\uc774 \uc11c\ub85c \ub3d9\ud615\uc774\ub77c\ub294 \ub73b\ub3c4 \uc544\ub2c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Benacerraf, P. (1965). \u201cWhat Numbers Could Not Be.\u201d The Philosophical Review, 74(1), 47\u201373.\" href=\"#ref-Benacerraf1965\">[Benacerraf1965]<\/a><a class=\"math-abs-series-ref\" title=\"Reck, E., &amp; Schiemer, G. (2021). \u201cStructuralism in the Philosophy of Mathematics.\u201d In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2021 ed.).\" href=\"#ref-ReckSchiemer2021\">[ReckSchiemer2021]<\/a> --><\/p>\n<p>\uadf8\ub7f0\ub370 \uc0b0\uc220\uc758 \uc5b8\uc5b4\uac00 \uc544\ub2c8\ub77c \uc9d1\ud569\ub860\uc758 \uc5b8\uc5b4\ub85c \u201c\\(1\\in3\\)\uc778\uac00?\u201d, \uc989 \u201c\uc790\uc5f0\uc218 \\(1\\)\uc744 \ub098\ud0c0\ub0b4\ub294 \uc9d1\ud569\uc774 \uc790\uc5f0\uc218 \\(3\\)\uc744 \ub098\ud0c0\ub0b4\ub294 \uc9d1\ud569\uc758 \uc6d0\uc18c\uc778\uac00?\u201d\ub77c\uace0 \ubb3c\uc73c\uba74 \ub2f5\uc774 \uac08\ub9b0\ub2e4. \ud3f0 \ub178\uc774\ub9cc \uad6c\ud604\uc5d0\uc11c\ub294 \\(3=\\{0,1,2\\}\\)\uc774\ubbc0\ub85c \\(1\\in3\\)\uc740 \ucc38\uc774\ub2e4. \ubc18\uba74 \uccb4\ub974\uba5c\ub85c \uad6c\ud604\uc5d0\uc11c\ub294 \\(3_Z=\\{2_Z\\}\\)\uc774\uace0 \\(1_Z\\neq2_Z\\)\uc774\ubbc0\ub85c \\(1_Z\\notin3_Z\\)\uc774\ub2e4. \uc774\ub294 \ub450 \uccb4\uacc4\uc758 \uc0b0\uc220\uc801 \ucc28\uc774\uac00 \uc544\ub2c8\ub77c \uc120\ud0dd\ud55c \uc9d1\ud569\ub860\uc801 \uad6c\ud604\uc5d0 \ub530\ub77c \ub367\ubd99\uc740 \uc131\uc9c8\uc758 \ucc28\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Benacerraf, P. (1965). \u201cWhat Numbers Could Not Be.\u201d The Philosophical Review, 74(1), 47\u201373.\" href=\"#ref-Benacerraf1965\">[Benacerraf1965]<\/a><\/p>\n<p>\ud3f4 \ubca0\ub098\uc138\ub77c\ud504(Paul Benacerraf)\ub294 1965\ub144 \ub17c\ubb38 \u201c\uc218\ub294 \ubb34\uc5c7\uc77c \uc218 \uc5c6\ub294\uac00\u201d(<i>What Numbers Could Not Be<\/i>)\uc5d0\uc11c \uc774\ub7ec\ud55c \ub2e4\uc911 \uad6c\ud604\uc744 \uc774\uc6a9\ud574 \uc790\uc5f0\uc218\ub97c \ud2b9\uc815 \uc9d1\ud569\ub4e4\uacfc \uc808\ub300\uc801\uc73c\ub85c \ub3d9\uc77c\uc2dc\ud558\ub294 \uacac\ud574\ub97c \ube44\ud310\ud588\ub2e4. \uadf8\uc758 \uc694\uc9c0\ub294 \uc0b0\uc220\uc5d0\uc11c \uc911\uc694\ud55c \uac83\uc740 \uac01 \uc218\ub97c \uc774\ub8e8\ub294 \uc9d1\ud569\uc758 \uc6d0\uc18c\uac00 \uc544\ub2c8\ub77c, \uc218\ub4e4\uc774 \ud55c \uc9c4\ud589\uc5f4\uc5d0\uc11c \uc11c\ub85c \ub9fa\ub294 \uad6c\uc870\uc801 \uad00\uacc4\ub77c\ub294 \uac83\uc774\ub2e4. \uc774 \ub17c\uc758\ub294 \uc218\ub97c \uad6c\uc870 \uc548\uc758 \uc704\uce58\ub85c \uc774\ud574\ud558\ub294 \uc218\ud559\uc801 \uad6c\uc870\uc8fc\uc758\uc5d0 \ud070 \uc601\ud5a5\uc744 \uc8fc\uc5c8\ub2e4. <!-- \uadf8\ub7ec\ub098 \uc774\ub97c \u2018\uc790\uc5f0\uc218 3\uc740 \uc5ed\ud560 \uadf8 \uc790\uccb4\ub2e4\u2019\ub77c\ub294 \ud55c \ubb38\uc7a5\uc758 \uc9c1\uc811 \uc778\uc6a9\uc73c\ub85c \uc81c\uc2dc\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4. \ub610\ud55c \ubca0\ub098\uc138\ub77c\ud504\uc758 \ub17c\uc99d\uc774 \ubaa8\ub4e0 \ud615\ud0dc\uc758 \uc9d1\ud569\ub860\uc801 \ud658\uc6d0\uc774\ub098 \uc218\ud559\uc801 \uad6c\uc870\uc8fc\uc758\uc5d0 \uad00\ud55c \ucca0\ud559\uc801 \ub17c\uc7c1\uc744 \ub05d\ub0b8 \uac83\ub3c4 \uc544\ub2c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Benacerraf, P. (1965). \u201cWhat Numbers Could Not Be.\u201d The Philosophical Review, 74(1), 47\u201373.\" href=\"#ref-Benacerraf1965\">[Benacerraf1965]<\/a><a class=\"math-abs-series-ref\" title=\"Reck, E., &amp; Schiemer, G. (2021). \u201cStructuralism in the Philosophy of Mathematics.\u201d In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2021 ed.).\" href=\"#ref-ReckSchiemer2021\">[ReckSchiemer2021]<\/a> --><\/p>\n<p>\uc774 \uc0ac\ub840\uc640 \uacf1\uc758 \ubcf4\ud3b8 \uc131\uc9c8\uc5d0\ub294 \uacf5\ud1b5\ub41c \ud1b5\ucc30\uc774 \uc788\ub2e4. \uc218\ud559\uc801\uc73c\ub85c \uc911\uc694\ud55c \ub3d9\uc77c\uc131\uc740 \uad6c\uccb4\uc801 \uad6c\ud604\uc758 \ubb38\uc790\uc801 \ub3d9\uc77c\uc131\uacfc \ub2e4\ub97c \uc218 \uc788\uace0, \uad00\ub828 \uad6c\uc870\uc640 \uc0ac\uc0c1\uc744 \ubcf4\uc874\ud558\ub294 \ub3d9\ud615\uc774 \ud575\uc2ec \uc5ed\ud560\uc744 \ud55c\ub2e4. <!-- \uadf8\ub7ec\ub098 \ubca0\ub098\uc138\ub77c\ud504\uc758 \ucca0\ud559\uc801 \ub17c\uc99d\uacfc \ubc94\uc8fc\ub860\uc758 \ubcf4\ud3b8 \uc131\uc9c8\uc774 \u2018\uc644\uc804\ud788 \ub3d9\uc77c\ud55c \uba85\uc81c\u2019\ub97c \uc99d\uba85\ud55c\ub2e4\uace0 \ub9d0\ud560 \uc218\ub294 \uc5c6\ub2e4. --> \uc804\uc790\ub294 \uc218\uc758 \uc874\uc7ac\ub860\uacfc \ub3d9\uc77c\uc131\uc5d0 \uad00\ud55c \ub17c\uc99d\uc774\uace0, \ud6c4\uc790\ub294 \ubc94\uc8fc \uc548\uc5d0\uc11c \ud2b9\uc815 \uad6c\uc131\uc744 \ud2b9\uc9d5\uc9d3\ub294 \uc218\ud559\uc801 \uc870\uac74\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><a class=\"math-abs-series-ref\" title=\"Benacerraf, P. (1965). \u201cWhat Numbers Could Not Be.\u201d The Philosophical Review, 74(1), 47\u201373.\" href=\"#ref-Benacerraf1965\">[Benacerraf1965]<\/a><a class=\"math-abs-series-ref\" title=\"Reck, E., &amp; Schiemer, G. (2021). \u201cStructuralism in the Philosophy of Mathematics.\u201d In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2021 ed.).\" href=\"#ref-ReckSchiemer2021\">[ReckSchiemer2021]<\/a><\/p>\n<p>[\uc694\ub124\ub2e4 \ubcf4\uc870\uc815\ub9ac(Yoneda lemma)\ub294 \u2018\uad00\uacc4\uac00 \ub300\uc0c1\uc744 \uacb0\uc815\ud55c\ub2e4\u2019\ub294 \uc9c1\uad00\uc5d0 \uc815\ubc00\ud55c \uc218\ud559\uc801 \ub0b4\uc6a9\uc744 \uc900\ub2e4. \uad6d\uc18c\uc801\uc73c\ub85c \uc791\uc740 \ubc94\uc8fc \\(\\mathcal C\\), \ub300\uc0c1 \\(A\\), \ud568\uc790 \\(F:\\mathcal C^{op}\\to\\mathrm{Set}\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[<br \/>\n\\operatorname{Nat}\\bigl(\\operatorname{Hom}_{\\mathcal C}(-,A),F\\bigr)\\cong F(A)<br \/>\n\\]<br \/>\n\ub77c\ub294 \uc790\uc5f0\uc2a4\ub7ec\uc6b4 \uc804\ub2e8\uc0ac\uac00 \uc131\ub9bd\ud55c\ub2e4. \uadf8 \uacb0\uacfc \uc694\ub124\ub2e4 \ub9e4\uc7a5<br \/>\n\\[<br \/>\n\\mathcal C\\longrightarrow \\mathrm{Set}^{\\mathcal C^{op}},\\qquad<br \/>\nA\\longmapsto\\operatorname{Hom}_{\\mathcal C}(-,A)<br \/>\n\\]<br \/>\n\uc740 \ucda9\uc2e4\ucda9\ub9cc\ud558\uace0, \ub450 \ub300\uc0c1\uc758 \ud45c\ud604\uac00\ub2a5 \ud568\uc790\uac00 \uc790\uc5f0\ub3d9\ud615\uc774\uba74 \ub450 \ub300\uc0c1\ub3c4 \ub3d9\ud615\uc774\ub2e4. \ub530\ub77c\uc11c \ub300\uc0c1\uc740 \ud569\uc131\uacfc \uc790\uc5f0\uc131\uae4c\uc9c0 \ud3ec\ud568\ud55c \u2018\ub4e4\uc5b4\uc624\ub294 \uc0ac\uc0c1\ub4e4\uc758 \uccb4\uacc4\u2019\ub85c \ub3d9\ud615\uae4c\uc9c0 \ubcf5\uc6d0\ub41c\ub2e4. \ub2e4\ub9cc \uc774 \uc815\ub9ac\uac00 \uc218\ud559\uc801 \uad6c\uc870\uc8fc\uc758\ub77c\ub294 \ucca0\ud559 \uc804\uccb4\ub97c \uc99d\uba85\ud558\uac70\ub098, \ub300\uc0c1\uc774 \ubb38\uc790 \uadf8\ub300\ub85c \uc0ac\uc0c1\ub4e4\uc758 \uc9d1\ud569\uc5d0 \ubd88\uacfc\ud558\ub2e4\uace0 \ub9d0\ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><a class=\"math-abs-series-ref\" title=\"Mac Lane, S. (1998). Categories for the Working Mathematician (2nd ed.). Springer.\" href=\"#ref-MacLane1998\">[MacLane1998]<\/a>]<\/p>\n<p>\ud504\ub808\uac8c\uac00 \uad6c\uccb4\uc801 \uc9c1\uc120 \uc790\uccb4\uac00 \uc544\ub2c8\ub77c \u2018\ud3c9\ud589\u2019\uc774\ub77c\ub294 \uad00\uacc4\ub97c \ud1b5\ud574 \uac19\uc740 \ubc29\ud5a5\uc744 \ubb36\uc73c\ub824 \ud588\ub358 \uc791\uc5c5\ub3c4, \uad6c\uccb4\uc801 \ud45c\ud604\uacfc \uad00\uacc4\uc801 \uc5ed\ud560\uc744 \uad6c\ubcc4\ud558\ub824\ub294 \ub354 \ub113\uc740 \uc5ed\uc0ac \uc18d\uc5d0\uc11c \uc774\ud574\ud560 \uc218 \uc788\ub2e4. <!-- \ub2e4\ub9cc \ud504\ub808\uac8c\uc758 \ucd94\uc0c1\ud654 \uc6d0\ub9ac, \ubca0\ub098\uc138\ub77c\ud504\uc758 \uad6c\uc870\uc8fc\uc758, \uc694\ub124\ub2e4 \ubcf4\uc870\uc815\ub9ac\ub294 \uc11c\ub85c \uad00\ub828\ub41c \ud1b5\ucc30\uc744 \uc81c\uacf5\ud560 \ubfd0 \ud558\ub098\uc758 \ub3d9\uc77c\ud55c \uc774\ub860\uc740 \uc544\ub2c8\ub2e4. --><\/p>\n<h4>\uadf8\ub85c\ud150\ub514\ud06c, \ubb38\uc81c\uac00 \uc800\uc808\ub85c \uc5f4\ub9ac\ub294 \uc9c0\uc810\uae4c\uc9c0<\/h4>\n<p>\ubc94\uc8fc\u00b7\ud568\uc790\u00b7\uce35\u00b7\ud638\ubab0\ub85c\uc9c0 \ub300\uc218\uc758 \uc5b8\uc5b4\ub97c \ub300\uc218\uae30\ud558\ud559\uc5d0\uc11c \ube44\uc57d\uc801\uc73c\ub85c \ud655\uc7a5\ud55c \uc911\uc2ec \uc778\ubb3c\uc740 \uc54c\ub809\uc0b0\ub354 \uadf8\ub85c\ud150\ub514\ud06c(Alexander Grothendieck)\uc774\ub2e4. \uadf8\ub294 1958\ub144\ubd80\ud130 1970\ub144\uae4c\uc9c0 IH\u00c9S\uc758 \uc0c1\uc784\uad50\uc218\ub85c \uc7ac\uc9c1\ud558\uba74\uc11c \uc7a5 \ub514\uc678\ub3c4\ub124(Jean Dieudonn\u00e9), \uc7a5\ud53c\uc5d0\ub974 \uc138\ub974(Jean-Pierre Serre), \ubbf8\ud558\uc5d8 \uc544\ub974\ud2f4(Michael Artin), \uc7a5\ub8e8\uc774 \ubca0\ub974\ub514\uc5d0(Jean-Louis Verdier) \ub4f1 \ub9ce\uc740 \ub3d9\ub8cc\uc640 \uc81c\uc790\ub4e4\uacfc \ud568\uaed8 \uc2a4\ud0b4, \ud45c\ud604\uac00\ub2a5 \ud568\uc790, \uce35 \ucf54\ud638\ubab0\ub85c\uc9c0, \uc5d0\ud0c8 \ucf54\ud638\ubab0\ub85c\uc9c0\uc640 \ud1a0\ud3ec\uc2a4 \ub4f1\uc758 \ud2c0\uc744 \ubc1c\uc804\uc2dc\ucf30\ub2e4. <!-- \uc774 \uc791\uc5c5\uc740 \ub300\uc218\uae30\ud558\ud559\uc758 \uc5b8\uc5b4\uc640 \uc5f0\uad6c \ubb38\uc81c\ub97c \ud06c\uac8c \ubc14\uafb8\uc5c8\uc9c0\ub9cc, \ud55c \uc0ac\ub78c\uc774 \ub300\uc218\uae30\ud558\ud559 \uc804\uccb4\ub97c \ubc11\ubc14\ub2e5\ubd80\ud130 \ub2e8\ub3c5\uc73c\ub85c \u2018\uc644\uc804\ud788 \uc7ac\uac74\ud588\ub2e4\u2019\uace0 \ud45c\ud604\ud558\uba74 \ud611\ub825\uc801 \uc131\uaca9\uacfc \uc138\ub974\ub97c \ube44\ub86f\ud55c \uc120\ud589 \uc5f0\uad6c\uac00 \uac00\ub824\uc9c4\ub2e4.<a class=\"math-abs-series-ref\" title=\"Institut des Hautes \u00c9tudes Scientifiques. \u201cAlexander Grothendieck, Permanent Professor from 1958 to 1970.\u201d\" href=\"#ref-IHESGrothendieck\">[IHESGrothendieck]<\/a><a class=\"math-abs-series-ref\" title=\"McLarty, C. (2007). \u201cThe Rising Sea: Grothendieck on Simplicity and Generality I.\u201d In J. J. Gray &amp; K. H. Parshall (Eds.), Episodes in the History of Recent Algebra, 301\u2013326. American Mathematical Society.\" href=\"#ref-McLarty2007\">[McLarty2007]<\/a> --><\/p>\n<p>[\u201c\ub300\uc218\uae30\ud558\ud559 \uc6d0\ub860\u201d(<i>\u00c9l\u00e9ments de g\u00e9om\u00e9trie alg\u00e9brique<\/i>, EGA)\uc740 \uadf8\ub85c\ud150\ub514\ud06c\uc640 \ub514\uc678\ub3c4\ub124\uc758 \uc774\ub984\uc73c\ub85c 1960\u20131967\ub144\uc5d0 \uc5ec\ub35f \ubd84\ucc45\uc73c\ub85c \ucd9c\ud310\ub41c, \ubcf8\ubb38 \ucabd\uc218\ub85c \uc57d 1,800\ucabd\uc5d0 \uc774\ub974\ub294 \ubbf8\uc644\uc131 \uc800\uc220\uc774\ub2e4. \u201c\ub300\uc218\uae30\ud558\ud559 \uc138\ubbf8\ub098\u201d(<i>S\u00e9minaire de g\u00e9om\u00e9trie alg\u00e9brique<\/i>, SGA)\ub294 1960\u20131969\ub144\uc758 \uc5ec\ub7ec \uc138\ubbf8\ub098\ub97c \ubc14\ud0d5\uc73c\ub85c \ub2e4\uc218\uc758 \uc218\ud559\uc790\uac00 \uc791\uc131\u00b7\ud3b8\uc9d1\ud558\uace0 \uc774\ud6c4 \uac1c\uc815\ud558\uc5ec \uc5ec\ub7ec \uad8c\uc73c\ub85c \ucd9c\ud310\ud55c \uae30\ub85d\uc774\ub2e4. \ub450 \ucd1d\uc11c\ub294 \ubc29\ub300\ud558\uc9c0\ub9cc \uc774\ub97c \ubaa8\ub450 \uadf8\ub85c\ud150\ub514\ud06c \ud55c \uc0ac\ub78c\uc758 \uc800\uc791\uc778 \u2018\uc218\ub9cc \ucabd\u2019\uc774\ub77c\uace0 \ubd80\ub974\ub294 \uac83\uc740 \uc800\uc790\u00b7\uc131\uaca9\u00b7\ubd84\ub7c9 \uba74\uc5d0\uc11c \ubd80\uc815\ud655\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Institut des Hautes \u00c9tudes Scientifiques. \u201cAlexander Grothendieck, Permanent Professor from 1958 to 1970.\u201d\" href=\"#ref-IHESGrothendieck\">[IHESGrothendieck]<\/a><a class=\"math-abs-series-ref\" title=\"Grothendieck, A., &amp; Dieudonn\u00e9, J. (1960). \u201c\u00c9l\u00e9ments de g\u00e9om\u00e9trie alg\u00e9brique I: Le langage des sch\u00e9mas.\u201d Publications Math\u00e9matiques de l\u2019IH\u00c9S, 4, 5\u2013228. Numdam.\" href=\"#ref-GrothendieckDieudonne1960\">[GrothendieckDieudonne1960]<\/a><a class=\"math-abs-series-ref\" title=\"Oort, F. (2014). \u201cDid Earlier Thoughts Inspire Grothendieck?\u201d In L. Schneps (Ed.), Alexandre Grothendieck: A Mathematical Portrait, 231\u2013268. International Press of Boston.\" href=\"#ref-Oort2014\">[Oort2014]<\/a><a class=\"math-abs-series-ref\" title=\"McLarty, C. (2007). \u201cThe Rising Sea: Grothendieck on Simplicity and Generality I.\u201d In J. J. Gray &amp; K. H. Parshall (Eds.), Episodes in the History of Recent Algebra, 301\u2013326. American Mathematical Society.\" href=\"#ref-McLarty2007\">[McLarty2007]<\/a>]<\/p>\n<p>\uadf8\ub85c\ud150\ub514\ud06c\ub294 1983\u20131986\ub144\uc5d0 \uc791\uc131\ud55c \ud68c\uace0\ub85d \u201c\uc218\ud655\uacfc \ud30c\uc885\u201d(<i>R\u00e9coltes et Semailles<\/i>)\uc5d0\uc11c \ubb38\uc81c\ub97c \ud478\ub294 \ub450 \ubc29\uc2dd\uc744 \ud638\ub450\uc5d0 \ube44\uc720\ud588\ub2e4. \ud55c \ubc29\uc2dd\uc740 \uc815\uacfc \ub9dd\uce58\ub85c \uaecd\ub370\uae30\ub97c \uc9c1\uc811 \uae68\ub294 \uac83\uc774\uace0, \ub2e4\ub978 \ubc29\uc2dd\uc740 \ud638\ub450\ub97c \ubb3c\uc5d0 \uc624\ub798 \ub2f4\uac00 \uaecd\ub370\uae30\uac00 \ubd80\ub4dc\ub7ec\uc6cc\uc9c4 \ub4a4 \uc190\uc73c\ub85c \uc5f4\ub9ac\uac8c \ud558\ub294 \uac83\uc774\ub2e4. \uc81c122\uc8fc\uc5d0\uc11c\ub294 \uc54c\uae30 \uc5b4\ub824\uc6b4 \uac83\uc744 \ub2e8\ub2e8\ud55c \ub545\uc5d0, \uc774\ub860\uc758 \uc77c\ubc18\uc131\uc774 \uc11c\uc11c\ud788 \uc790\ub77c\ub294 \uacfc\uc815\uc744 \uc18c\ub9ac \uc5c6\uc774 \ucc28\uc624\ub974\ub294 \ubc14\ub2e4\uc5d0 \ube44\uc720\ud588\ub2e4. \uc774\ub294 \u2018\ucd94\uc0c1\ud654\ud558\uba74 \ubaa8\ub4e0 \ubb38\uc81c\uac00 \uc790\ub3d9\uc73c\ub85c \ud480\ub9b0\ub2e4\u2019\ub294 \uacf5\uc2dd\uc774 \uc544\ub2c8\ub77c, \uc9c1\uc811 \ud0c0\uaca9\uacfc \uc7a5\uae30\uac04\uc758 \uac1c\ub150 \ud615\uc131\uc774\ub77c\ub294 \uc11c\ub85c \ub2e4\ub978 \uc5f0\uad6c \uc2a4\ud0c0\uc77c\uc744 \uc124\uba85\ud558\ub294 \uc790\uc804\uc801 \uc740\uc720\ub2e4.<a class=\"math-abs-series-ref\" title=\"McLarty, C. (2007). \u201cThe Rising Sea: Grothendieck on Simplicity and Generality I.\u201d In J. J. Gray &amp; K. H. Parshall (Eds.), Episodes in the History of Recent Algebra, 301\u2013326. American Mathematical Society.\" href=\"#ref-McLarty2007\">[McLarty2007]<\/a><\/p>\n<p>\uadf8 \ubc29\ubc95\ub860\uacfc \uc5f0\uacb0\ub418\ub294 \uc911\uc694\ud55c \uc5ed\uc0ac\uc801 \uc0ac\ub840\uac00 <span class=\"defined\">\ubca0\uc720 \ucd94\uce21<\/span>(Weil conjectures)\uc774\ub2e4. \uc559\ub4dc\ub808 \ubca0\uc720\ub294 1949\ub144 \uc720\ud55c\uccb4 \uc704 \ub300\uc218\ub2e4\uc591\uccb4\uc758 \uc810 \uac1c\uc218\ub97c \ubd80\ud638\ud654\ud55c \uc81c\ud0c0\ud568\uc218\uc5d0 \uad00\ud558\uc5ec \uc720\ub9ac\uc131, \ud568\uc218\ubc29\uc815\uc2dd\uacfc \ubca0\ud2f0 \uc218\uc5d0 \ub300\uc751\ud558\ub294 \ucc28\uc218, \uadf8\ub9ac\uace0 \ub9ac\ub9cc \uac00\uc124\ud615 \uc808\ub313\uac12 \uc870\uac74\uc744 \uc81c\uc2dc\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Weil, A. (1949). \u201cNumbers of Solutions of Equations in Finite Fields.\u201d Bulletin of the American Mathematical Society, 55(5), 497\u2013508.\" href=\"#ref-Weil1949\">[Weil1949]<\/a><\/p>\n<p>\ud574\uacb0\uc758 \uacf5\ub85c\ub294 \ud55c \uc0ac\ub78c\uc774\ub098 \ud55c \uc774\ub860\uc5d0\ub9cc \ub3cc\uc544\uac00\uc9c0 \uc54a\ub294\ub2e4. \ubca0\ub974\ub098\ub974 \ub4dc\uc6cc\ud06c(Bernard Dwork)\ub294 1960\ub144 \\(p\\)-\uc9c4 \ud574\uc11d\uc744 \uc0ac\uc6a9\ud558\uc5ec \uc720\ub9ac\uc131\uc744 \uba3c\uc800 \uc99d\uba85\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Dwork, B. (1960). \u201cOn the Rationality of the Zeta Function of an Algebraic Variety.\u201d American Journal of Mathematics, 82(3), 631\u2013648.\" href=\"#ref-Dwork1960\">[Dwork1960]<\/a> \uadf8\ub85c\ud150\ub514\ud06c, \ubbf8\ud558\uc5d8 \uc544\ub974\ud2f4, \uc7a5\ub8e8\uc774 \ubca0\ub974\ub514\uc5d0\uc640 \uc5ec\ub7ec \ud611\ub825\uc790\uac00 \ubc1c\uc804\uc2dc\ud0a8 \uc5d0\ud0c8 \ucf54\ud638\ubab0\ub85c\uc9c0 \ubc0f \uadf8 \ucd94\uc801 \uacf5\uc2dd\uc740 \uc720\ub9ac\uc131, \ud568\uc218\ubc29\uc815\uc2dd, \ubca0\ud2f0 \uc218\uc640\uc758 \ub300\uc751\uc744 \ud558\ub098\uc758 \ucf54\ud638\ubab0\ub85c\uc9c0\uc801 \ud2c0\uc5d0\uc11c \uc124\uba85\ud588\ub2e4. \ub9c8\uc9c0\ub9c9\uc73c\ub85c \ud53c\uc5d0\ub974 \ub4e4\ub9ac\ub274(Pierre Deligne)\ub294 1973\ub144\uc5d0 \ub9ac\ub9cc \uac00\uc124\ud615 \ubd80\ubd84\uc758 \uc99d\uba85\uc744 \uc644\uc131\ud558\uace0 1974\ub144\uc5d0 \ubc1c\ud45c\ud588\ub2e4. \uadf8\ub294 \uc5d0\ud0c8 \ucf54\ud638\ubab0\ub85c\uc9c0\uc758 \ud2c0\uc744 \uc0ac\uc6a9\ud588\uc9c0\ub9cc, \uadf8\ub85c\ud150\ub514\ud06c\uac00 \uc81c\uc548\ud55c \ud45c\uc900 \ucd94\uce21\uc744 \uba3c\uc800 \uc99d\uba85\ud558\ub294 \uacbd\ub85c\ub97c \ub530\ub974\uc9c0\ub294 \uc54a\uc558\ub2e4.<a class=\"math-abs-series-ref\" title=\"McLarty, C. (2007). \u201cThe Rising Sea: Grothendieck on Simplicity and Generality I.\u201d In J. J. Gray &amp; K. H. Parshall (Eds.), Episodes in the History of Recent Algebra, 301\u2013326. American Mathematical Society.\" href=\"#ref-McLarty2007\">[McLarty2007]<\/a><a class=\"math-abs-series-ref\" title=\"Deligne, P. (1974). \u201cLa conjecture de Weil. I.\u201d Publications Math\u00e9matiques de l\u2019IH\u00c9S, 43, 273\u2013307.\" href=\"#ref-Deligne1974\">[Deligne1974]<\/a> <!-- \ub530\ub77c\uc11c \uc774 \uc131\uacfc\ub294 \u2018\ubc94\uc8fc\ub860\uc774 \ubb38\uc81c\ub97c \ub300\uc2e0 \ud480\uc5c8\ub2e4\u2019\uae30\ubcf4\ub2e4, \ubca0\uc720\uc758 \ud1b5\ucc30, \ub4dc\uc6cc\ud06c\uc758 \ub3c5\ub9bd\uc801\uc778 \\(p\\)-\uc9c4 \ubc29\ubc95, \uadf8\ub85c\ud150\ub514\ud06c \ud559\ud30c\uc758 \ucf54\ud638\ubab0\ub85c\uc9c0 \uc774\ub860, \ub4e4\ub9ac\ub274\uc758 \uc0c8\ub85c\uc6b4 \ub17c\uc99d\uc774 \ud569\ub958\ud55c \uacb0\uacfc\ub85c \ubcf4\uc544\uc57c \ud55c\ub2e4. --><\/p>\n<h4>\uc6d0\uc18c\uc640 \uc0ac\uc0c1, \uad6c\ud604\uacfc \uc5ed\ud560<\/h4>\n<p>\uc9c0\uae08\uae4c\uc9c0\uc758 \ud750\ub984\uc740 \ub300\uc0c1\uc5d0\uc11c \uad6c\uc870\ub85c, \uad6c\uc870\uc5d0\uc11c \uc0ac\uc0c1\uc73c\ub85c \uace7\uac8c \ubed7\uc740 \ud558\ub098\uc758 \uacc4\ub2e8\uc774\ub77c\uae30\ubcf4\ub2e4 \uc5ec\ub7ec \uc5f0\uad6c \uc804\ud1b5\uc774 \uad50\ucc28\ud55c \uc5ed\uc0ac\ub2e4.<\/p>\n<ul>\n<li>\ud790\ubca0\ub974\ud2b8\ub294 \ubd88\ubcc0\ub7c9 \uc774\ub860\uc5d0\uc11c \uc544\uc774\ub514\uc5bc\uc758 \uc720\ud55c\uc131\uc744 \uc774\uc6a9\ud55c \uc874\uc7ac \ub17c\uc99d\uc744 \uc81c\uc2dc\ud588\uace0, \ub1cc\ud130\ub294 \uc624\ub984\uc0ac\uc2ac\uc870\uac74\uc744 \uc77c\ubc18 \uac00\ud658\ub300\uc218\uc758 \uac15\ub825\ud55c \uc870\uc9c1 \uc6d0\ub9ac\ub85c \ubc1c\uc804\uc2dc\ucf30\ub2e4.<\/li>\n<li>\ud310\ub370\ub974\ubc14\ub974\ub358\uc740 \ub1cc\ud130\uc640 \uc544\ub974\ud2f4\uc744 \ube44\ub86f\ud55c \uc5ec\ub7ec \uc5f0\uad6c\uc758 \uc131\uacfc\ub97c \u201cModerne Algebra\u201d\uc5d0 \uc885\ud569\ud558\uc5ec \uad6c\uc870\uc801 \ub300\uc218\ud559\uc758 \uad50\uacfc\uc11c \ubaa8\ud615\uc744 \ub110\ub9ac \ud655\uc0b0\uc2dc\ucf30\ub2e4.<\/li>\n<li>\ubd80\ub974\ubc14\ud0a4\ub294 \uacf5\ub9ac\uc640 \uad6c\uc870\ub97c \uc218\ud559\uc758 \ud1b5\uc77c\uc131\uc744 \uc124\uba85\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc73c\ub85c \uc81c\uc2dc\ud588\uc9c0\ub9cc, \uc138 \ubaa8\uad6c\uc870\ub294 \uc644\uacb0\ub41c \ubd84\ub958 \uc815\ub9ac\uac00 \uc544\ub2c8\uc5c8\uace0 \ubc94\uc8fc\ub860\uacfc\uc758 \uad00\uacc4\ub3c4 \ub2e8\uc21c\ud55c \ub300\ub9bd\uc740 \uc544\ub2c8\uc5c8\ub2e4.<\/li>\n<li>\uc544\uc77c\ub80c\ubca0\ub974\ud06c\uc640 \ub9e4\ud074\ub808\uc778\uc740 \ub300\uc0c1\uacfc \uc0ac\uc0c1\uc744 \ud568\uaed8 \uace0\ub824\ud558\ub294 \ubc94\uc8fc\u00b7\ud568\uc790\u00b7\uc790\uc5f0 \ubcc0\ud658\uc758 \uc5b8\uc5b4\ub97c \ub9cc\ub4e4\uc5c8\uace0, \uacf1\uc758 \ubcf4\ud3b8 \uc131\uc9c8\uc740 \uad6c\uccb4\uc801 \uad6c\ud604\uacfc \ubc94\uc8fc\uc801 \uc5ed\ud560\uc744 \uad6c\ubcc4\ud558\ub294 \ubc29\ubc95\uc744 \ubcf4\uc5ec \uc900\ub2e4.<\/li>\n<li>\ud3f0 \ub178\uc774\ub9cc\uc2dd \uc790\uc5f0\uc218\uc640 \uccb4\ub974\uba5c\ub85c\uc2dd \uc790\uc5f0\uc218\uc758 \ube44\uad50\ub294 \uac19\uc740 \uc0b0\uc220 \uad6c\uc870\uac00 \uc11c\ub85c \ub2e4\ub978 \uc9d1\ud569\ub860\uc801 \uad6c\ud604\uc744 \uac00\uc9c8 \uc218 \uc788\uc74c\uc744 \ubcf4\uc5ec \uc8fc\uba70, \ubca0\ub098\uc138\ub77c\ud504\ub294 \uc774 \uc0ac\uc2e4\uc5d0\uc11c \uc601\ud5a5\ub825 \uc788\uc9c0\ub9cc \ub17c\uc7c1\uc801\uc778 \uad6c\uc870\uc8fc\uc758\uc801 \uacb0\ub860\uc744 \ub04c\uc5b4\ub0c8\ub2e4.<\/li>\n<li>\uadf8\ub85c\ud150\ub514\ud06c\uc640 \ud611\ub825\uc790\ub4e4\uc740 \ubc94\uc8fc\ub860\uc801\u00b7\ucf54\ud638\ubab0\ub85c\uc9c0\uc801 \uc5b8\uc5b4\ub97c \ub300\uc218\uae30\ud558\ud559\uc758 \uc2e4\uc81c \ubb38\uc81c\uc5d0 \uc801\uc6a9\ud588\uace0, \ubca0\uc720 \ucd94\uce21\uc758 \ud574\uacb0\uc740 \uc5ec\ub7ec \uc218\ud559\uc790\uc758 \uc11c\ub85c \ub2e4\ub978 \ubc29\ubc95\uc774 \ud569\ub958\ud55c \ub300\ud45c\uc801 \uc0ac\ub840\uac00 \ub418\uc5c8\ub2e4.<\/li>\n<\/ul>\n<p><span class=\"defined\">\ubcf4\ud3b8 \uc131\uc9c8\uc744 \uc0ac\uc6a9\ud55c \uc815\uc758<\/span>\ub294 \ud2b9\uc815\ud55c \ub0b4\ubd80 \uad6c\ud604\uc744 \uba3c\uc800 \uace0\uc815\ud558\uc9c0 \uc54a\uace0, \ud55c \ub300\uc0c1\uacfc \uc0ac\uc0c1\ub4e4\uc774 \ubc94\uc8fc \uc548\uc5d0\uc11c \ub9cc\uc871\ud558\ub294 \uc874\uc7ac\uc131\uacfc \uc720\uc77c\uc131 \uc870\uac74\uc73c\ub85c \uadf8 \ub300\uc0c1\uc744 \ub3d9\ud615\uae4c\uc9c0 \ud2b9\uc9d5\uc9d3\ub294 \ubc29\ubc95\uc774\ub2e4. \uc9d1\ud569\uc758 \uacf1\uc5d0\uc11c\ub294 \uc21c\uc11c\uc30d \uad6c\uc131\uc774 \uc5ec\uc804\ud788 \uacf1\uc758 \ud55c \uc720\uc6a9\ud55c \ubaa8\ud615\uc774\uc9c0\ub9cc, \ubcf4\ud3b8 \uc131\uc9c8 \ub355\ubd84\uc5d0 \uadf8 \uad6c\ud604\uc5d0 \uc758\uc874\ud558\uc9c0 \uc54a\ub294 \uc815\ub9ac\ub4e4\uc744 \ub9d0\ud560 \uc218 \uc788\ub2e4.<a class=\"math-abs-series-ref\" title=\"Riehl, E. (2016). Category Theory in Context. Dover Publications.\" href=\"#ref-Riehl2016\">[Riehl2016]<\/a><a class=\"math-abs-series-ref\" title=\"Mac Lane, S. (1998). Categories for the Working Mathematician (2nd ed.). Springer.\" href=\"#ref-MacLane1998\">[MacLane1998]<\/a><\/p>\n<p>\uc774 \uc5f0\uc7ac\uc5d0\uc11c\ub294 \uc9c0\uae08\uae4c\uc9c0 \ub2e4\uc74c \uc138 \uac00\uc9c0\ub97c \ud575\uc2ec\uc801\uc778 \ucd94\uc0c1\ud654 \ubc29\uc2dd\uc73c\ub85c \uc815\ub9ac\ud588\ub2e4.<\/p>\n<ul>\n<li>\ub3d9\uce58\ub958\ub97c \uc0ac\uc6a9\ud55c \uc815\uc758<\/li>\n<li>\uacf5\ub9ac\ud654<\/li>\n<li>\ubcf4\ud3b8 \uc131\uc9c8\uc744 \uc0ac\uc6a9\ud55c \uc815\uc758<\/li>\n<\/ul>\n<p>\uc774 \uc138 \uac00\uc9c0 \ubc29\uc2dd\uc740 \ubcf8 \uc5f0\uc7ac\uc5d0\uc11c \ub2e4\ub8ec \ucd94\uc0c1\ud654\uc758 \ud750\ub984\uc744 \uc774\ud574\ud558\ub294 \ud575\uc2ec\uc801\uc778 \ud2c0\uc774\ub2e4. \ub3d9\uce58\ub958\ub294 \ub3d9\uc77c\uc131 \uc870\uac74\uc5d0 \ub530\ub77c \uc5ec\ub7ec \ud45c\ud604\uc744 \ubb36\uace0, \uacf5\ub9ac\ud654\ub294 \ub300\uc0c1\ub4e4\uc774 \ub9cc\uc871\ud574\uc57c \ud560 \ubc95\uce59\uc744 \ubd84\ub9ac\ud558\uba70, \ubcf4\ud3b8 \uc131\uc9c8\uc740 \uc0ac\uc0c1\ub4e4\uc758 \uc874\uc7ac\uc131\uacfc \uc720\uc77c\uc131\uc73c\ub85c \uad6c\uc131\uc744 \ud2b9\uc9d5\uc9d3\ub294\ub2e4. \uc2e4\uc81c \uc218\ud559\uc5d0\uc11c\ub294 \uc138 \ubc29\uc2dd\uc774 \uc11c\ub85c \uacb9\uccd0 \uc0ac\uc6a9\ub418\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<p>\uc774\uc81c \uc2dc\uc120\uc744 \uac70\uc2dc\uc801\uc778 \uc218\ud559\uc0ac\uc5d0\uc11c \ud558\ub098\uc758 \uad6c\uccb4\uc801\uc778 \ud559\ubd80 \uac15\uc758\uc2e4\ub85c \uc881\ud600 \ubcf4\uc790. 19\uc138\uae30\uae4c\uc9c0 \uc11c\ub85c \ub2e4\ub978 \ub9e5\ub77d\uc5d0\uc11c \uc5f0\uad6c\ub418\ub358 \uc5f0\ub9bd\ubc29\uc815\uc2dd\uc758 \ud574, \uae30\ud558\ud559\uc758 \ubca1\ud130, \ud568\uc218\uc640 \ubbf8\ubd84\ubc29\uc815\uc2dd\uc758 \ud574\uac00 \uc5b4\ub5bb\uac8c <span class=\"defined\">\ubca1\ud130\uacf5\uac04<\/span>(vector space)\uc774\ub77c\ub294 \ud558\ub098\uc758 \ub300\uc218\uc801 \uad6c\uc870 \uc544\ub798 \ube44\uad50\ub420 \uc218 \uc788\uac8c \ub418\uc5c8\ub294\uc9c0, <a href=\"..\/math-abstraction-06-vector-spaces\/\">6\ubd80<\/a>\uc5d0\uc11c \uadf8 \uacfc\uc815\uc744 \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<h4>\ucc38\uace0\ubb38\ud5cc<\/h4>\n<ul>\n<li id=\"ref-Hilbert1890\">[Hilbert1890] Hilbert, D. (1890). \u201cUeber die Theorie der algebraischen Formen.\u201d <i>Mathematische Annalen<\/i>, 36, 473\u2013534. <a href=\"https:\/\/doi.org\/10.1007\/BF01208503\">https:\/\/doi.org\/10.1007\/BF01208503<\/a>.<\/li>\n<li id=\"ref-McLarty2012\">[McLarty2012] McLarty, C. (2012). \u201cHilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics.\u201d In A. Doxiadis &amp; B. Mazur (Eds.), <i>Circles Disturbed: The Interplay of Mathematics and Narrative<\/i>, 105\u2013129. Princeton University Press. <a href=\"https:\/\/doi.org\/10.1515\/9781400842681.105\">https:\/\/doi.org\/10.1515\/9781400842681.105<\/a>.<\/li>\n<li id=\"ref-Noether1921\">[Noether1921] Noether, E. (1921). \u201cIdealtheorie in Ringbereichen.\u201d <i>Mathematische Annalen<\/i>, 83, 24\u201366. <a href=\"https:\/\/doi.org\/10.1007\/BF01464225\">https:\/\/doi.org\/10.1007\/BF01464225<\/a>. \uc601\uc5b4 \ubc88\uc5ed: <a href=\"https:\/\/arxiv.org\/abs\/1401.2577\">arXiv:1401.2577<\/a>.<\/li>\n<li id=\"ref-StacksProject\">[StacksProject] The Stacks Project Authors. \u201cNoetherian rings.\u201d <i>The Stacks Project<\/i>, Tag 00FM. <a href=\"https:\/\/stacks.math.columbia.edu\/tag\/00FM\">https:\/\/stacks.math.columbia.edu\/tag\/00FM<\/a>.<\/li>\n<li id=\"ref-VanDerWaerden1975\">[VanDerWaerden1975] van der Waerden, B. L. (1975). \u201cOn the Sources of My Book Moderne Algebra.\u201d <i>Historia Mathematica<\/i>, 2(1), 31\u201340. <a href=\"https:\/\/doi.org\/10.1016\/0315-0860(75)90034-8\">https:\/\/doi.org\/10.1016\/0315-0860(75)90034-8<\/a>.<\/li>\n<li id=\"ref-Corry2004\">[Corry2004] Corry, L. (2004). <i>Modern Algebra and the Rise of Mathematical Structures<\/i> (2nd rev. ed.). Birkh\u00e4user. <a href=\"https:\/\/doi.org\/10.1007\/978-3-0348-7917-0\">https:\/\/doi.org\/10.1007\/978-3-0348-7917-0<\/a>.<\/li>\n<li id=\"ref-BourbakiAssociation\">[BourbakiAssociation] Association des collaborateurs et collaboratrices de Nicolas Bourbaki. \u201cFounding Members.\u201d <a href=\"https:\/\/www.bourbaki.fr\/index-en.html\">https:\/\/www.bourbaki.fr\/index-en.html<\/a>.<\/li>\n<li id=\"ref-Beaulieu1993\">[Beaulieu1993] Beaulieu, L. (1993). \u201cA Parisian Caf\u00e9 and Ten Proto-Bourbaki Meetings (1934\u20131935).\u201d <i>The Mathematical Intelligencer<\/i>, 15, 27\u201335. <a href=\"https:\/\/doi.org\/10.1007\/BF03025255\">https:\/\/doi.org\/10.1007\/BF03025255<\/a>.<\/li>\n<li id=\"ref-Bourbaki1950\">[Bourbaki1950] Bourbaki, N. (1950). \u201cThe Architecture of Mathematics.\u201d <i>The American Mathematical Monthly<\/i>, 57(4), 221\u2013232. <a href=\"https:\/\/doi.org\/10.1080\/00029890.1950.11999523\">https:\/\/doi.org\/10.1080\/00029890.1950.11999523<\/a>.<\/li>\n<li id=\"ref-Corry1992\">[Corry1992] Corry, L. (1992). \u201cNicolas Bourbaki and the Concept of Mathematical Structure.\u201d <i>Synthese<\/i>, 92, 315\u2013348. <a href=\"https:\/\/doi.org\/10.1007\/BF00414286\">https:\/\/doi.org\/10.1007\/BF00414286<\/a>.<\/li>\n<li id=\"ref-EilenbergMacLane1945\">[EilenbergMacLane1945] Eilenberg, S., &amp; Mac Lane, S. (1945). \u201cGeneral Theory of Natural Equivalences.\u201d <i>Transactions of the American Mathematical Society<\/i>, 58(2), 231\u2013294. <a href=\"https:\/\/doi.org\/10.1090\/S0002-9947-1945-0013131-6\">https:\/\/doi.org\/10.1090\/S0002-9947-1945-0013131-6<\/a>.<\/li>\n<li id=\"ref-MacLane1997\">[MacLane1997] Mac Lane, S. (1997). \u201cThe PNAS Way Back Then.\u201d <i>Proceedings of the National Academy of Sciences<\/i>, 94(12), 5983\u20135985. <a href=\"https:\/\/doi.org\/10.1073\/pnas.94.12.5983\">https:\/\/doi.org\/10.1073\/pnas.94.12.5983<\/a>.<\/li>\n<li id=\"ref-Riehl2016\">[Riehl2016] Riehl, E. (2016). <i>Category Theory in Context<\/i>. Dover Publications. <a href=\"https:\/\/emilyriehl.github.io\/files\/context.pdf\">https:\/\/emilyriehl.github.io\/files\/context.pdf<\/a>.<\/li>\n<li id=\"ref-MacLane1998\">[MacLane1998] Mac Lane, S. (1998). <i>Categories for the Working Mathematician<\/i> (2nd ed.). Springer. <a href=\"https:\/\/doi.org\/10.1007\/978-1-4757-4721-8\">https:\/\/doi.org\/10.1007\/978-1-4757-4721-8<\/a>.<\/li>\n<li id=\"ref-VonNeumann1923\">[VonNeumann1923] von Neumann, J. (1923). \u201cZur Einf\u00fchrung der transfiniten Zahlen.\u201d <i>Acta Scientiarum Mathematicarum (Szeged)<\/i>, 1(4), 199\u2013208. <a href=\"https:\/\/acta.bibl.u-szeged.hu\/13294\/1\/math_001_199-208.pdf\">https:\/\/acta.bibl.u-szeged.hu\/13294\/1\/math_001_199-208.pdf<\/a>.<\/li>\n<li id=\"ref-Zermelo1908\">[Zermelo1908] Zermelo, E. (1908). \u201cUntersuchungen \u00fcber die Grundlagen der Mengenlehre. I.\u201d <i>Mathematische Annalen<\/i>, 65, 261\u2013281. <a href=\"https:\/\/doi.org\/10.1007\/BF01449999\">https:\/\/doi.org\/10.1007\/BF01449999<\/a>.<\/li>\n<li id=\"ref-Benacerraf1965\">[Benacerraf1965] Benacerraf, P. (1965). \u201cWhat Numbers Could Not Be.\u201d <i>The Philosophical Review<\/i>, 74(1), 47\u201373. <a href=\"https:\/\/doi.org\/10.2307\/2183530\">https:\/\/doi.org\/10.2307\/2183530<\/a>.<\/li>\n<li id=\"ref-ReckSchiemer2021\">[ReckSchiemer2021] Reck, E., &amp; Schiemer, G. (2021). \u201cStructuralism in the Philosophy of Mathematics.\u201d In E. N. Zalta (Ed.), <i>The Stanford Encyclopedia of Philosophy<\/i> (Winter 2021 ed.). <a href=\"https:\/\/plato.stanford.edu\/archives\/win2021\/entries\/structuralism-mathematics\/\">https:\/\/plato.stanford.edu\/archives\/win2021\/entries\/structuralism-mathematics\/<\/a>.<\/li>\n<li id=\"ref-IHESGrothendieck\">[IHESGrothendieck] &#8220;>Institut des Hautes \u00c9tudes Scientifiques. \u201cAlexander Grothendieck, Permanent Professor from 1958 to 1970.\u201d <a href=\"https:\/\/www.ihes.fr\/en\/professeur\/alexander-grothendieck-1\/\">https:\/\/www.ihes.fr\/en\/professeur\/alexander-grothendieck-1\/<\/a>.<\/li>\n<li id=\"ref-GrothendieckDieudonne1960\">[GrothendieckDieudonne1960] Grothendieck, A., &amp; Dieudonn\u00e9, J. (1960). \u201c\u00c9l\u00e9ments de g\u00e9om\u00e9trie alg\u00e9brique I: Le langage des sch\u00e9mas.\u201d <i>Publications Math\u00e9matiques de l\u2019IH\u00c9S<\/i>, 4, 5\u2013228. <a href=\"https:\/\/www.numdam.org\/item\/PMIHES_1960__4__5_0\/\">Numdam<\/a>.<\/li>\n<li id=\"ref-Oort2014\">[Oort2014] Oort, F. (2014). \u201cDid Earlier Thoughts Inspire Grothendieck?\u201d In L. Schneps (Ed.), <i>Alexandre Grothendieck: A Mathematical Portrait<\/i>, 231\u2013268. International Press of Boston. <a href=\"https:\/\/webspace.science.uu.nl\/~oort0109\/AGRoots-final.pdf\">https:\/\/webspace.science.uu.nl\/~oort0109\/AGRoots-final.pdf<\/a>.<\/li>\n<li id=\"ref-McLarty2007\">[McLarty2007] McLarty, C. (2007). \u201cThe Rising Sea: Grothendieck on Simplicity and Generality I.\u201d In J. J. Gray &amp; K. H. Parshall (Eds.), <i>Episodes in the History of Recent Algebra<\/i>, 301\u2013326. American Mathematical Society. <a href=\"https:\/\/doi.org\/10.1090\/HMATH\/032\/14\">https:\/\/doi.org\/10.1090\/HMATH\/032\/14<\/a>.<\/li>\n<li id=\"ref-Weil1949\">[Weil1949] Weil, A. (1949). \u201cNumbers of Solutions of Equations in Finite Fields.\u201d <i>Bulletin of the American Mathematical Society<\/i>, 55(5), 497\u2013508. <a href=\"https:\/\/doi.org\/10.1090\/S0002-9904-1949-09219-4\">https:\/\/doi.org\/10.1090\/S0002-9904-1949-09219-4<\/a>.<\/li>\n<li id=\"ref-Dwork1960\">[Dwork1960] Dwork, B. (1960). \u201cOn the Rationality of the Zeta Function of an Algebraic Variety.\u201d <i>American Journal of Mathematics<\/i>, 82(3), 631\u2013648. <a href=\"https:\/\/doi.org\/10.2307\/2372974\">https:\/\/doi.org\/10.2307\/2372974<\/a>.<\/li>\n<li id=\"ref-Deligne1974\">[Deligne1974] Deligne, P. (1974). \u201cLa conjecture de Weil. I.\u201d <i>Publications Math\u00e9matiques de l\u2019IH\u00c9S<\/i>, 43, 273\u2013307. <a href=\"https:\/\/doi.org\/10.1007\/BF02684373\">https:\/\/doi.org\/10.1007\/BF02684373<\/a>.<\/li>\n<\/ul>\n<h4>\uc800\uc791\uad8c<\/h4>\n<p>\uc774\uc2ac\ube44, 2026. designeralice\uff20daum.net.<\/p>\n<div class=\"math-abs-series-contents\">\n<p class=\"math-abs-series-menu-title\"><a href=\"..\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654<\/a><\/p>\n<ol class=\"math-abs-series-menu-list\">\n        <!-- \ud604\uc7ac \ud398\uc774\uc9c0\uc5d0 \ud574\ub2f9\ud558\ub294 li \ud0dc\uadf8\uc5d0 class=\"math-abs-series-current-page\" \uc18d\uc131 \ucd94\uac00 --><\/p>\n<li><a href=\"..\/math-abstraction-01-essence\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uae30\ubcf8 \uac1c\ub150<\/a><\/li>\n<li><a href=\"..\/math-abstraction-02-implicit-era\/\">\ucd08\uae30 \uc218\ud559\uc5d0\uc11c\uc758 \uc554\ubb35\uc801 \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-03-algebraic-symbols\/\">\ub300\uc218\uc801 \uae30\ud638\uc640 \uc5f0\uc0b0 \ubc95\uce59<\/a><\/li>\n<li><a href=\"..\/math-abstraction-04-axiomatic-method\/\">\uacf5\ub9ac\uc801 \ubc29\ubc95\uc5d0 \uc758\ud55c \ucd94\uc0c1\ud654<\/a><\/li>\n<li class=\"math-abs-series-current-page\"><a href=\"..\/math-abstraction-05-mathematical-structures\/\">\uc218\ud559\uc801 \uad6c\uc870\uc640 \ubc94\uc8fc\ub860<\/a><\/li>\n<li><a href=\"..\/math-abstraction-06-vector-spaces\/\">\ubca1\ud130\uacf5\uac04\uacfc \uc120\ud615 \uad6c\uc870<\/a><\/li>\n<li><a href=\"..\/math-abstraction-07-topological-spaces\/\">\uac70\ub9ac\uacf5\uac04\uacfc \uc704\uc0c1\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-08-measure-spaces\/\">\uce21\ub3c4\uacf5\uac04\uacfc \ud655\ub960\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-09-cognitive-process\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uc778\uc9c0\uc640 \ud559\uc2b5<\/a><\/li>\n<li><a href=\"..\/math-abstraction-10-optimal-generality\/\">\ud604\ub300 \uc218\ud559 \uc5f0\uad6c\uc5d0\uc11c\uc758 \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-11-topography\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \ubc29\ubc95\uacfc \ucca0\ud559<\/a><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p><!-- class=\"math-abs-series\" --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uad70\uc758 \uacf5\ub9ac, \ud658\uc758 \uacf5\ub9ac, \uccb4\uc758 \uacf5\ub9ac\ucc98\ub7fc \uc11c\ub85c \ub2e4\ub978 \uc774\ub860\uc5d0\uc11c \uc138\uc6cc\uc9c4 \uacf5\ub9ac \uccb4\uacc4\ub4e4\uc744 \ub354 \ub113\uc740 \uad00\uc810\uc5d0\uc11c \ube44\uad50\ud558\uba74 \ubb34\uc5c7\uc744 \ubcfc \uc218 \uc788\uc744\uae4c? 20\uc138\uae30 \uc804\ubc18\uc758 \ub300\uc218\ud559\uc790\ub4e4\uacfc \ubd80\ub974\ubc14\ud0a4\ub294 \uc5ec\ub7ec \uc218\ud559 \ubd84\uc57c\ub97c \uad6c\uc870(structure)\uc640 \uadf8 \uad6c\uc870\ub97c \ubcf4\uc874\ud558\ub294 \ub300\uc751\uc758 \uad00\uc810\uc5d0\uc11c \uc870\uc9c1\ud558\ub294 \ub370 \ud06c\uac8c \uae30\uc5ec\ud588\ub2e4. \ud55c\ud3b8 1940\ub144\ub300\uc5d0 \ub4f1\uc7a5\ud55c \ubc94\uc8fc\ub860\uc740 \uc790\uc5f0\uc131, \ud568\uc790, \uc0ac\uc0c1\uacfc \ubcf4\ud3b8 \uc131\uc9c8\uc744 \uc0c8\ub85c\uc6b4 \uacf5\ud1b5 \uc5b8\uc5b4\ub85c \uc81c\uc2dc\ud588\ub2e4. \uc774 \uae00\uc5d0\uc11c\ub294 \ub450 \ud750\ub984\uc774 \uac01\uac01 \uc5b4\ub5a4 \ubb38\uc81c\uc5d0\uc11c \ucd9c\ubc1c\ud588\uace0 \uc5b4\ub5bb\uac8c \uc11c\ub85c \ub2e4\ub978 \ucd94\uc0c1\ud654\uc758 \uc5b8\uc5b4\ub97c \uc81c\uacf5\ud588\ub294\uc9c0&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":9726,"menu_order":500,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"no","_lmt_disable":"","footnotes":""},"class_list":["post-9743","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9743","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=9743"}],"version-history":[{"count":28,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9743\/revisions"}],"predecessor-version":[{"id":10052,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9743\/revisions\/10052"}],"up":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/pages\/9726"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=9743"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}