{"id":33134,"date":"2022-03-16T21:06:39","date_gmt":"2022-03-16T13:06:39","guid":{"rendered":"https:\/\/swarma.org\/?p=33134"},"modified":"2022-03-16T21:06:39","modified_gmt":"2022-03-16T13:06:39","slug":"%e8%8c%83%e7%95%b4%e8%ae%ba%ef%bc%9a%e8%bf%88%e5%90%91%e6%95%b0%e5%ad%a6%e7%9a%84%e7%bb%9f%e4%b8%80","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=33134","title":{"rendered":"\u8303\u7574\u8bba\uff1a\u8fc8\u5411\u6570\u5b66\u7684\u7edf\u4e00"},"content":{"rendered":"
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\u590f\u5c14\u00b7\u57c3\u96f7\u65af\u66fc\uff08Charles Ehresmann\uff09 | \u4f5c\u8005<\/span><\/strong><\/p>\n

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\u672c\u6587\u662f\u590f\u5c14\u00b7\u57c3\u96f7\u65af\u66fc\uff08Charles Ehresmann\uff0c1905-1979\uff09\u4e8e1966\u5e744\u670825\u65e5\u5728\u582a\u8428\u65af\u5927\u5b66\u52b3\u4f26\u65af\u5206\u6821\u6570\u5b66\u7cfb\u8363\u8a89\u665a\u5bb4\u4e0a\u7684\u6f14\u8bb2\uff0c\u540c\u5e74\u53d1\u8868\u4e8eCahiers de topologie et g\u00e9om\u00e9trie diff\u00e9rentielle cat\u00e9goriques (\u300a\u8303\u7574\u62d3\u6251\u5b66\u4e0e\u8303\u7574\u5fae\u5206\u51e0\u4f55\u300b) \u6742\u5fd7\uff0c\u9898\u76ee\u4e3a\u201cTrends toward unity in mathematics\u201d\u3002\u57c3\u96f7\u65af\u66fc\u662f\u4e00\u4f4d\u5728\u5fb7\u56fd\u51fa\u751f\u7684\u6cd5\u56fd\u6570\u5b66\u5bb6\uff0c\u4ed6\u662f\u5e03\u5c14\u5df4\u57fa\u5b66\u6d3e\u7684\u65e9\u671f\u6210\u5458\u4e4b\u4e00\uff0c\u5728\u5fae\u5206\u62d3\u6251\u548c\u8303\u7574\u8bba\u7b49\u9886\u57df\u4f5c\u51fa\u4e86\u91cd\u8981\u5de5\u4f5c\u3002<\/span><\/p>\n


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19\u4e16\u7eaa\u7531\u7f57\u5df4\u5207\u592b\u65af\u57fa\u548c\u4e9a\u8bfa\u4ec0[6]\u5206\u522b\u72ec\u7acb\u53d1\u73b0\u7684\u975e\u6b27\u51e0\u91cc\u5f97\u51e0\u4f55\u5b66\u662f\u53e6\u4e00\u8fdb\u6b65\u3002\u622a\u6b62\u90a3\u65f6\uff0c\u53e4\u5178\u65f6\u4ee3\u4e3a\u6570\u5b66\u6240\u8bbe\u4e0b\u7684\u6240\u6709\u754c\u9650\u90fd\u88ab\u6253\u7834\u4e86\uff1a<\/span>\uff08\u6b27\u51e0\u91cc\u5f97\uff09<\/span>\u51e0\u4f55\u5b66\u4e0d\u518d\u662f\u7531\u611f\u77e5\u7ecf\u9a8c\u6240\u5f3a\u52a0\u7ed9\u6211\u4eec\u7684\uff0c\u5176\u6240\u4f9d\u8d56\u7684\u662f\u4eba\u7c7b\u57fa\u4e8e\u516c\u7406\u7684\u521b\u9020\uff1b\u6211\u4eec\u53ef\u4ee5\u8bbe\u60f3\u4e0d\u540c\u7684\u516c\u7406\u7cfb\u7edf\u6765\u7814\u7a76\u4e0d\u540c\u7684\u51e0\u4f55\u5b66\u3002\u5eb7\u5fb7\u6240\u5f3a\u8c03\u7684\u6211\u4eec\u5bf9\u4e8e\u7a7a\u95f4\u6982\u5ff5\u7684\u201c\u5148\u9a8c\u6027<\/span>\uff08a priori\uff09<\/span>\u201d\u7531\u6b64\u53d8\u5f97\u8fc7\u65f6\u4e86[7]\u3002\u90a3\u4e48\uff0c\u51e0\u4f55\u5b66\u7684\u672c\u8d28\u5230\u5e95\u662f\u4ec0\u4e48\uff1f\u5728\u5f53\u65f6\uff0c\u4eba\u4eec\u5c06\u4e00\u4e2a\u5177\u6709\u4f20\u9012\u6027\u7fa4\u4f5c\u7528\u7684\u7a7a\u95f4\u4f5c\u4e3a\u51e0\u4f55\u7684\u7edf\u4e00\u6027\u6982\u5ff5\uff0c\u4f8b\u5982\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u7684\u4f20\u9012\u7fa4\u4f5c\u7528\u4e8b\u5b9e\u4e0a\u5c31\u662f\u6b27\u51e0\u91cc\u5f97\u5e73\u79fb\u53d8\u6362\u3002\u56e0\u6b64\uff0c\u51e0\u4f55\u5b66\u6210\u4e3a\u4e00\u4e2a\u7fa4\u4f5c\u7528\u7684\u4e0d\u53d8\u91cf\u548c\u5171\u53d8\u4f53\u7684\u7406\u8bba\u3002\u4f46\u5b9e\u9645\u4e0a\uff0c\u8fd9\u4e2a\u5b9a\u4e49\u53ea\u9002\u7528\u4e8e\u9f50\u6027\u7a7a\u95f4\u4e2d\u7684\u51e0\u4f55\u5b66\uff0c\u800c\u5176\u4ed6\u7c7b\u578b\u7684\u51e0\u4f55\u5df2\u88ab\u53d1\u73b0\uff0c\u4eba\u4eec\u611f\u5230\u6709\u5fc5\u8981\u5bf9\u51e0\u4f55\u548c\u7a7a\u95f4\u7684\u6982\u5ff5\u8fdb\u884c\u53e6\u5916\u7684\u6982\u62ec\u3002\u8fd9\u6700\u7ec8\u5bfc\u81f4\u4e86\u62d3\u6251\u7a7a\u95f4\u7684\u5b9a\u4e49\uff0c\u5b83\u662f\u56de\u7b54\u6240\u6709\u5173\u4e8e\u8fde\u7eed\u6027\u3001\u6781\u9650\u548c\u8fd1\u4f3c\u95ee\u9898\u7684\u6070\u5f53\u8bed\u5883\uff0c\u4e5f\u4f7f\u5f97\u5206\u6790\u548c\u51e0\u4f55\u9886\u57df\u4e2d\u8bb8\u591a\u5171\u540c\u7684\u7ed3\u6784\u5f97\u4ee5\u663e\u73b0\u3002<\/span><\/section>\n

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[1] \u4ea8\u5229\u00b7\u67cf\u683c\u68ee (Henri Bergson, 1859-1941)\uff0c\u6cd5\u56fd\u54f2\u5b66\u5bb6\uff0c\u6587\u5b66\u5bb6\uff0c\u4e8e1927\u5e74\u51ed\u501f\u4e30\u5bcc\u3001\u5bcc\u6709\u6d3b\u529b\u7684\u601d\u60f3\u548c\u8bed\u8a00\u83b7\u5f97\u8bfa\u8d1d\u5c14\u6587\u5b66\u5956\uff08\u8bd1\u8005\u6ce8\uff1b\u5168\u6587\u6240\u6709\u7684\u811a\u6ce8\u5747\u4e3a\u8bd1\u8005\u6240\u52a0\uff0c\u540e\u4e0d\u518d\u4e00\u4e00\u6307\u660e\uff09\u3002<\/span><\/section>\n
[2] \u6b27\u591a\u514b\u7d22\u65af\uff08Eudoxus\uff0c408 B.C.\u2013355 B.C. \uff09\uff0c\u53e4\u5e0c\u814a\u6570\u5b66\u5bb6\u3001\u5929\u6587\u5b66\u5bb6\uff0c\u6b27\u51e0\u91cc\u5f97\u300a\u51e0\u4f55\u539f\u672c\u300b\u4e2d\u7684\u8bb8\u591a\u5185\u5bb9\u5f88\u6709\u53ef\u80fd\u662f\u6765\u6e90\u4e8e\u6b27\u591a\u514b\u7d22\u65af\uff0c\u4e00\u4e9b\u4eba\u8ba4\u4e3a\u4ed6\u662f\u53e4\u5e0c\u814a\u6700\u6770\u51fa\u7684\u6570\u5b66\u5bb6\u3002<\/span><\/section>\n
[3] \u91cc\u67e5\u5fb7\u00b7\u6234\u5f97\u91d1\uff08Richard Dedekind\uff0c1831-1916\uff09\uff0c\u5fb7\u56fd\u6570\u5b66\u5bb6\uff0c\u5728\u6570\u8bba\u3001\u62bd\u8c61\u4ee3\u6570\uff08\u7279\u522b\u662f\u73af\u8bba\uff09\u4ee5\u53ca\u7b97\u6570\u7684\u516c\u7406\u5316\u7b49\u9886\u57df\u4f5c\u51fa\u975e\u5e38\u91cd\u8981\u7684\u8d21\u732e\u3002<\/span><\/section>\n
[4] \u5f17\u6717\u7d22\u74e6\u00b7\u97e6\u8fbe\uff08Fran\u00e7ois Vi\u00e8te\uff0c1540-1603\uff09\uff0c\u6cd5\u56fd\u6570\u5b66\u5bb6\uff0c\u521d\u9ad8\u4e2d\u751f\u4eec\u719f\u6089\u7684\u97e6\u8fbe\u5b9a\u7406\u5c31\u6765\u6e90\u4e8e\u4ed6\u3002<\/span><\/section>\n
[5] \u901a\u7528\u8868\u610f\u6587\u5b57 \uff08\u62c9\u4e01\u8bed\u4e3acharacteristica universalis\uff09\uff0c\u662f\u83b1\u5e03\u5c3c\u8328\u6240\u8bbe\u60f3\u7684\u4e00\u79cd\u901a\u7528\u7684\u5f62\u5f0f\u5316\u8bed\u8a00\uff0c\u8be5\u8bed\u8a00\u80fd\u591f\u8868\u8fbe\u6570\u5b66\u3001\u79d1\u5b66\u4ee5\u53ca\u5f62\u800c\u4e0a\u5b66\u7b49\u65b9\u9762\u7684\u6982\u5ff5\uff0c\u5e76\u652f\u6301\u4e00\u79cd\u901a\u7528\u7684\u903b\u8f91\u6f14\u7b97\u3002<\/span><\/section>\n
[6] \u5c3c\u53e4\u62c9\u00b7\u7f57\u5df4\u5207\u592b\u65af\u57fa\uff08Nikolai Lobachevsky\uff0c1792-1856 \uff09\uff0c\u4fc4\u56fd\u6570\u5b66\u5bb6\uff1b\u9c8d\u8036\u00b7\u4e9a\u8bfa\u4ec0\uff08J\u00e1nos Bolyai, 1802-1860\uff09\uff0c\u5308\u7259\u5229\u6570\u5b66\u5bb6\uff0c\u4ed6\u4eec\u548c\u9ad8\u65af\u751f\u6d3b\u5728\u540c\u4e00\u65f6\u4ee3\u3002\u4e24\u4eba\u5747\u72ec\u7acb\u7684\u4e3a\u975e\u6b27\u51e0\u4f55\uff0c\u7279\u522b\u662f\u53cc\u66f2\u51e0\u4f55\uff0c\u4f5c\u51fa\u4e86\u91cd\u8981\u8d21\u732e\u3002<\/span><\/section>\n
[7] \u5eb7\u5fb7\u8ba4\u4e3a\u4eba\u7c7b\u5bf9\u65f6\u95f4\u548c\u7a7a\u95f4\u7684\u8ba4\u8bc6\u4e0d\u662f\u901a\u8fc7\u6982\u5ff5\u5316\uff08conceptualisation\uff09\u7684\u65b9\u5f0f\u5b8c\u6210\u7684\uff0c\u5b83\u4eec\u662f\u6211\u4eec\u611f\u89c2\u76f4\u89c9\u7684\u7eaf\u7cb9\u5f62\u5f0f\uff08pure form of sensible intuition\uff09\u3002\u975e\u5e38\u7c97\u7565\u5730\u6765\u8bf4\uff0c\u524d\u8005\u6d89\u53ca\u77e5\u6027\uff08understanding\uff09\u7684\u8fd0\u4f5c\uff0c\u800c\u540e\u8005\u5f62\u6210\u7684\u77e5\u8bc6\u5219\u662f\u5148\u9a8c\u7684\u3002<\/span><\/section>\n
[8] \u683c\u5965\u5c14\u683c\u00b7\u5eb7\u6258\u5c14\uff08Georg Cantor\uff0c1845-1918\uff09\uff0c\u662f\u51fa\u751f\u4e8e\u4fc4\u56fd\u7684\u5fb7\u56fd\u6570\u5b66\u5bb6\uff0c\u521b\u7acb\u4e86\u73b0\u4ee3\u96c6\u5408\u8bba\uff0c\u662f\u5b9e\u6570\u7684\u4e25\u683c\u5b9a\u4e49\u53ca\u6574\u4e2a\u5fae\u79ef\u5206\u4f53\u7cfb\u7684\u7406\u8bba\u57fa\u7840\uff0c\u4e3a\u6570\u5b66\u57fa\u7840\uff08foundation of mathematics\uff09\u4f5c\u51fa\u4e86\u6770\u51fa\u7684\u8d21\u732e\u3002<\/span><\/section>\n
[9] \u8fd9\u91cc\u6307\u672c\u6587\u6210\u6587\u7684\u65f6\u95f4\uff0c\u537320\u4e16\u7eaa\u3002<\/span><\/section>\n
[10] \u5c3c\u53e4\u62c9\u00b7\u5e03\u5c14\u5df4\u57fa\uff08Nicolas Bourbaki\uff09\u662f20\u4e16\u7eaa\u4e00\u7fa4\u6cd5\u56fd\u6570\u5b66\u5bb6\u7684\u5171\u540c\u7b14\u540d\uff0c\u4ed6\u4eec\u81ea1935\u5e74\u5f00\u59cb\u64b0\u5199\u4e00\u7cfb\u5217\u5173\u4e8e\u73b0\u4ee3\u9ad8\u7b49\u6570\u5b66\u7684\u4e66\u7c4d\uff0c\u4ee5\u628a\u6240\u6709\u6570\u5b66\u5efa\u7acb\u5728\u96c6\u5408\u8bba\u575a\u5b9e\u7684\u57fa\u7840\u4e4b\u4e0a\u4e3a\u76ee\u7684\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u4ed6\u4eec\u81f4\u529b\u4e8e\u5c06\u6570\u5b66\u6982\u5ff5\u5c3d\u53ef\u80fd\u5730\u666e\u904d\u5316\u548c\u4e25\u8c28\u5316\uff0c \u5bf920\u4e16\u7eaa\u4e4b\u540e\u7684\u6570\u5b66\u53d1\u5c55\u4ea7\u751f\u4e86\u6df1\u523b\u7684\u5f71\u54cd\u3002<\/span><\/section>\n
[11] \u8303\u7574\u8bba\u6700\u65e9\u8d77\u6e90\u4e8e1945\u5e74Eilenberg\u548cMacLane \u7684\u9898\u4e3aGeneral Theory of Natural Equivalences\u7684\u8bba\u6587\uff0c\u5728\u968f\u540e\u7684\u51e0\u5341\u5e74\u5185\u4f5c\u4e3a\u4e00\u95e8\u6570\u5b66\u8bed\u8a00\u548c\u5de5\u5177\u8fc5\u901f\u5730\u53c2\u4e0e\u5230\u5404\u4e2a\u6570\u5b66\u5206\u652f\u7684\u53d1\u5c55\u4e4b\u4e2d\u3002\u9057\u61be\u7684\u662f\uff0c\u672c\u6587\u4f5c\u8005\u57c3\u96f7\u65af\u66fc\u7684\u8fd9\u4e00\u731c\u6d4b\u76f4\u5230\u591a\u5e74\u540e\u7684\u4eca\u5929\u4e5f\u6ca1\u80fd\u5728\u5927\u591a\u6570\u7684\u5927\u5b66\u5185\u6210\u4e3a\u73b0\u5b9e\u3002<\/span><\/section>\n
[12] \u5728\u73b0\u4ee3\u7684\u8303\u7574\u8bba\u8bed\u8a00\u4e2d\uff0c\u4e00\u822c\u628a\u8303\u7574\u5b9a\u4e49\u4e3a\u4e24\u79cd\u7c7b\u522b\u7684\u5143\u7d20\uff0c\u5373\u7269\u4f53\u548c\u5b83\u4eec\u4e4b\u95f4\u7684\u6001\u5c04\uff0c\u6240\u6784\u6210\u7684\u6570\u5b66\u5bf9\u8c61\uff1b\u4f46\u4e5f\u53ef\u4ee5\u4ec5\u4ec5\u5c06\u4e00\u4e2a\u8303\u7574\u7406\u89e3\u4e3a\u4e00\u65cf\u6001\u5c04\u52a0\u4e0a\u4e0a\u9762\u90e8\u5206\u5b9a\u4e49\u7684\u590d\u5408\u64cd\u4f5c\uff0c\u56e0\u4e3a\u8303\u7574\u4e2d\u7684\u7269\u4f53\u548c\u5355\u4f4d\u6001\u5c04\u662f\u4e00\u4e00\u5bf9\u5e94\u7684\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6001\u5c04\u7684\u4fe1\u606f\u5305\u542b\u4e86\u7269\u4f53\u7684\u4fe1\u606f\u3002\u672c\u6587\u5bf9\u8303\u7574\u6240\u91c7\u53d6\u7684\u662f\u540e\u4e00\u79cd\u7406\u89e3\u3002<\/span><\/section>\n
[13] \u5373\u628a\u4e00\u4e2a\u540c\u6001\u770b\u4f5c\u662f\u5176\u5bf9\u5e94\u7684\u96c6\u5408\u4e4b\u95f4\u7684\u51fd\u6570\u3002<\/span><\/section>\n

<\/section>\n
\u672c\u6587\u8bd1\u81ea Ehresmann Charles. “Trends toward unity in mathematics.” Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques 8 (1966): 1-7.<\/span><\/section>\n

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\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n


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\u8303\u7574\u8bba\uff1a\u8de8\u5b66\u79d1\u7684\u79d1\u5b66\u65b9\u6cd5\u8bba
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\u6301\u7eed\u62a5\u540d\u4e2d<\/span><\/strong>
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\u8bfe\u7a0b\u5927\u7eb2\uff08\u7b2c\u4e00\u5b63\uff09\uff1a<\/span><\/strong><\/p>\n

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  1. \n

    \u7ebf\u6027\u4ee3\u6570\u2014\u2014\u8303\u7574\u7684\u89c6\u89d2<\/span><\/p>\n<\/li>\n

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    \u96c6\u5408\u8303\u7574\u548c\u7b49\u4ef7\u5173\u7cfb<\/span><\/p>\n<\/li>\n

  3. \n

    \u504f\u5e8f\u96c6\u8303\u7574<\/span><\/p>\n<\/li>\n

  4. \n

    Abel\u7fa4\u8303\u7574<\/span><\/p>\n<\/li>\n

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    \u7ebf\u6027\u7a7a\u95f4\u7684\u8303\u7574\u5316\u6784\u9020<\/span><\/p>\n<\/li>\n

  6. \n

    Hom\u51fd\u5b50<\/span><\/p>\n<\/li>\n

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    \u7ebf\u6027\u7a7a\u95f4\u7684\u5bf9\u5076\u6027<\/span><\/p>\n<\/li>\n

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    \u6b63\u5411\u6781\u9650\u4e0e\u9006\u5411\u6781\u9650<\/span><\/p>\n<\/li>\n

  9. \n

    \u6b63\u5408<\/span><\/p>\n<\/li>\n

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    \u4ece\u96c6\u5408\u5230\u62d3\u6251\u7a7a\u95f4<\/span><\/p>\n<\/li>\n

  11. \n

    \u81ea\u7531\u51fd\u5b50<\/span><\/p>\n<\/li>\n

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    \u4ece\u51e0\u4f55\u5230\u4ee3\u6570\u2014\u2014\u540c\u8c03\u7fa4\u7684\u6784\u9020<\/span><\/section>\n<\/li>\n<\/ol>\n


    <\/h3>\n

    \u8bfe\u7a0b\u5927\u7eb2\uff08\u7b2c\u4e8c\u5b63\uff09\uff1a<\/span><\/strong>
    <\/h3>\n
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    1. \n

      \u7528\u7bad\u5934\u6784\u9020\u77e9\u9635\uff08\u514d\u8d39\u516c\u5f00\uff09<\/span><\/p>\n<\/li>\n

    2. \n

      \u51fd\u5b50\u8303\u7574\uff08\u514d\u8d39\u516c\u5f00\uff09<\/span><\/p>\n<\/li>\n

    3. \n

      \u53ef\u8868\u51fd\u5b50I<\/span><\/p>\n<\/li>\n

    4. \n

      \u53ef\u8868\u51fd\u5b50II<\/span><\/p>\n<\/li>\n

    5. \n

      Yoneda\u5f15\u7406<\/span><\/p>\n<\/li>\n

    6. \n

      \u4f34\u968f\u51fd\u5b50<\/span><\/p>\n<\/li>\n

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    8. \n

      \u5f20\u91cf\u4ee3\u6570<\/span><\/p>\n<\/li>\n

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      \u5e7a\u534a\u8303\u7574<\/span><\/p>\n<\/li>\n

    10. \n

      \u5355\u5b50<\/span><\/p>\n<\/li>\n

    11. \n

      \u6cdb\u6027\u8d28<\/span><\/p>\n<\/li>\n

    12. \n
      Abel\u8303\u7574<\/span><\/section>\n<\/li>\n<\/ol>\n


      <\/p>\n

      \u8bfe\u7a0b\u76ee\u7684<\/span><\/strong><\/p>\n