{"id":26638,"date":"2021-05-31T21:37:07","date_gmt":"2021-05-31T13:37:07","guid":{"rendered":"https:\/\/swarma.org\/?p=26638"},"modified":"2021-05-31T21:37:07","modified_gmt":"2021-05-31T13:37:07","slug":"%e4%ba%ba%e4%ba%ba%e5%8f%af%e5%ad%a6%e7%9a%84%e8%8c%83%e7%95%b4%e8%ae%ba-%e8%b7%a8%e9%a2%86%e5%9f%9f%e7%9a%84%e7%a7%91%e5%ad%a6%e6%96%b9%e6%b3%95%e8%ae%ba-%e7%b2%be%e5%93%81","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=26638","title":{"rendered":"\u4eba\u4eba\u53ef\u5b66\u7684\u8303\u7574\u8bba\u2014\u2014\u8de8\u9886\u57df\u7684\u79d1\u5b66\u65b9\u6cd5\u8bba | \u7cbe\u54c1\u5165\u95e8\u7cfb\u5217\u8bfe"},"content":{"rendered":"
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\u8303\u7574\u8bba\u662f\u4e00\u4e2a\u7814\u7a76\u7ed3\u6784\u7684\u7406\u8bba\uff0c\u63d0\u4f9b\u4e86\u4e00\u79cd\u7cfb\u7edf\u3001\u7cbe\u786e\u3001\u62bd\u8c61\u7684\u8de8\u9886\u57df\u79d1\u5b66\u65b9\u6cd5\u8bba\uff0c\u53ef\u76f4\u63a5\u4ed8\u8bf8\u4e8e\u5404\u9886\u57df\u8003\u5bdf\u7684\u95ee\u9898\uff0c\u5bfb\u6c42\u8de8\u9886\u57df\u7684\u89e3\u51b3\u4e4b\u9053\u3002\u8fd9\u79cd\u6570\u5b66\u8bed\u8a00\u4e0e\u590d\u6742\u6027\u79d1\u5b66\u6709\u4f17\u591a\u76f8\u4f3c\u4e4b\u5904\uff0c\u52a0\u4e4b\u5176\u672c\u8eab\u4f5c\u4e3a\u6570\u5b66\u5de5\u5177\u7684\u4e25\u5bc6\u6027\uff0c\u540e\u7eed\u53ef\u80fd\u80fd\u4e3a\u89e3\u51b3\u590d\u6742\u6027\u79d1\u5b66\u95ee\u9898\u63d0\u4f9b\u4e00\u628a\u94a5\u5319\u3002<\/span><\/strong><\/p>\n


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\u4e3a\u4e86\u8ba9\u5927\u5bb6\u4e86\u89e3\u8303\u7574\u8bba\u8fd9\u6837\u4e00\u95e8\u73b0\u4ee3\u6570\u5b66\u8bed\u8a00\uff0c\u514b\u670d\u4f20\u7edf\u5b66\u4e60\u8303\u7574\u8bba\u62bd\u8c61\u548c\u5bf9\u524d\u7f6e\u77e5\u8bc6\u7684\u969c\u788d\uff0c\u96c6\u667a\u5b66\u56ed\u7279\u9080\u4e00\u4f4d\u6b63\u5728\u5c1d\u8bd5\u6559\u4e2d\u5b66\u751f\u8303\u7574\u8bba\u7684J-CAT\u732b\u5708\u8001\u5e08\u5f00\u8bfe\uff0c\u7b79\u5212\u4e86\u201c\u96c6\u667a\u8303\u7574\u8bba\u5165\u95e8\u7cfb\u5217\u8bfe\u7a0b\u201d\u3002\u5e0c\u671b\u8fd9\u95e8\u8bfe\u7a0b\u53ef\u4ee5\u5e2e\u52a9\u5927\u5bb6\u7834\u9664\u95e8\u69db\uff0c\u987a\u5229\u5165\u95e8\u3002\u6b64\u7cfb\u5217\u8bfe\u7a0b\u4e3a\u5468\u66f4\u8bfe\u7a0b\uff0c\u6bcf\u5468\u65e5\u4e2d\u534812\u70b9\u66f4\u65b0\uff0c\u9996\u6b21\u5f00\u653e\u56db\u8282\uff0c\u6b22\u8fce\u5bf9\u8303\u7574\u8bba\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\u52a0\u5165\u8bfe\u7a0b\u3002<\/strong><\/p>\n


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\u7279\u522b\u63d0\u9192\uff1a\u6211\u4eec\u4e5f\u4e3a\u5927\u5bb6\u63d0\u4f9b\u4e86\u4ea4\u6d41\u7684\u5fae\u4fe1\u7fa4\uff0c\u8bf7\u62a5\u540d\u7684\u5c0f\u4f19\u4f34\uff0c\u5728\u62a5\u540d\u9875\u9762\uff0c\u627e\u5230\u5e76\u6dfb\u52a0\u52a9\u6559\u5fae\u4fe1\u54e6\uff0c\u671f\u5f85\u4f60\u7684\u52a0\u5165\u3002<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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\u8303\u7574\u8bba\u63d0\u4f9b\u4e86\u7cfb\u7edf\u3001\u7cbe\u786e\u3001\u62bd\u8c61\u7684\u8de8\u9886\u57df\u79d1\u5b66\u65b9\u6cd5\u8bba\u3002\u4e0d\u540c\u77e5\u8bc6\u9886\u57df\u7684\u95ee\u9898\u6309\u7167\u7279\u5b9a\u7684\u8303\u7574\u6765\u7ec4\u7ec7\uff0c\u8303\u7574\u8bba\u901a\u8fc7\u51fd\u5b50\u6765\u8fde\u63a5\u4e0d\u540c\u9886\u57df\u7684\u4e0d\u540c\u8303\u7574\uff0c\u5b9e\u73b0\u8de8\u9886\u57df\u7684\u7814\u7a76\u3002\u51fd\u5b50\u628a\u6e90\u8303\u7574\u7684\u7ed3\u6784\u6620\u5c04\u5230\u76ee\u6807\u8303\u7574\u3002\u590d\u6742\u7684\u8303\u7574\u53ef\u80fd\u8f6c\u5316\u5230\u7b80\u5355\u7684\u8303\u7574\uff0c\u964c\u751f\u7684\u8303\u7574\u53ef\u80fd\u8f6c\u5316\u5230\u719f\u6089\u7684\u9886\u57df\u4e2d\u7684\u8303\u7574\uff0c\u62bd\u8c61\u7684\u8303\u7574\u53ef\u80fd\u8f6c\u5316\u5230\u6613\u4e8e\u8ba1\u7b97\u7684\u8303\u7574\u3002<\/span><\/span><\/p>\n


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\u8303\u7574\u8bba\u5c3d\u53ef\u80fd\u5730\u7528\u51fd\u5b50\u6765\u6784\u9020\u8fd9\u79cd\u8de8\u8303\u7574\u7684\u8054\u7cfb\uff0c\u6784\u9020\u4e00\u4e2a\u597d\u7684\u51fd\u5b50\uff0c\u628a\u539f\u6709\u9886\u57df\u8303\u7574\u91cd\u8981\u7684\u7ed3\u6784\u4fe1\u606f\uff0c\u66f4\u591a\u5730\u4fdd\u6301\u5230\u76ee\u6807\u8303\u7574\u4e2d\u3002\u5177\u4f53\u6784\u9020\u65f6\u5c31\u9700\u8981\u7279\u5b9a\u9886\u57df\u7684\u77e5\u8bc6\u4e86\u3002<\/span><\/p>\n


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\u5728\u8303\u7574\u8bba\u53d1\u660e\u524d\uff0c\u5e76\u6ca1\u6709\u7cfb\u7edf\u5316\u7684\u8de8\u9886\u57df\u8054\u7cfb\u7684\u65b9\u6cd5\u8bba\uff0c\u8bb8\u591a\u79d1\u5b66\u7684\u8fdb\u5c55\u90fd\u4f9d\u9760\u79d1\u5b66\u5bb6\u5929\u624d\u7684\u8054\u60f3\u80fd\u529b\u3002\u6bd4\u5982 Galois \u5bf9\u7fa4\u548c\u57df\u8fd9\u4e24\u4e2a\u8303\u7574\u7684\u8054\u60f3\uff0c\u4fc3\u8fdb\u4e86\u6570\u8bba\u548c\u7fa4\u8bba\u7684\u5927\u5e45\u53d1\u5c55\u3002\u5982\u4eca\u5728\u8303\u7574\u8bba\u4e2d\u8fd9\u79cd\u8054\u60f3\u7cfb\u7edf\u5316\u5730\u53d1\u5c55\u6210\u4e3a\u4e86 Galois \u8fde\u63a5\u3002<\/span><\/p>\n


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\u4e0e\u81ea\u7136\u8bed\u8a00\u63cf\u8ff0\u4e3a\u4e3b\u7684\u79d1\u5b66\u54f2\u5b66\u4e0d\u540c\uff0c\u8303\u7574\u8bba\u662f\u6570\u5b66\u9886\u57df\u62bd\u8c61\u7a0b\u5ea6\u7684\u9876\u5cf0\uff0c\u662f\u53ef\u4ee5\u4ee5\u516c\u5f0f\u6216\u8005\u5176\u5b83\u6570\u5b66\u8868\u8fbe\u65b9\u5f0f\u660e\u786e\u6307\u5bfc\u5177\u4f53\u7814\u7a76\u7684\u3002<\/span>\u5b66\u4e60\u8303\u7574\u8bba\u7684\u8fc7\u7a0b\uff0c\u4e5f\u662f\u5728\u4f53\u9a8c\u7cfb\u7edf\u3001\u7cbe\u786e\u3001\u62bd\u8c61\u7684\u79d1\u5b66\u65b9\u6cd5\u8bba\u3002<\/span>\u7406\u89e3\u8303\u7574\u8bba\u4fc3\u8fdb\u5b66\u79d1\u8054\u7cfb\u7684\u8fc7\u7a0b\uff0c\u5e76\u4ed8\u8bf8\u5404\u9886\u57df\u8003\u5bdf\u7684\u95ee\u9898\uff0c\u6709\u671b\u5bfb\u627e\u5230\u8de8\u9886\u57df\u7684\u89e3\u51b3\u4e4b\u9053\u3002<\/span><\/p>\n


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\u8303\u7574\u8bba\u4f55\u4ee5\u8bde\u751f\u5e76\u53d1\u5c55<\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


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\u8303\u7574\u8bba\u8bde\u751f\u4e8e 20 \u4e16\u7eaa 40 \u5e74\u4ee3\uff0c\u80cc\u666f\u662f\u4eba\u4eec\u8bd5\u56fe\u7528\u66f4\u7b80\u5355\u7684\u4ee3\u6570\u65b9\u6cd5\u6765\u89e3\u51b3\u4e00\u4e2a\u56f0\u96be\u7684\u62d3\u6251\u95ee\u9898\u3002<\/span><\/p>\n


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\u4e0a\u4e16\u7eaa\u521d\u51e0\u4f55\u5b66\u7684\u53d1\u5c55\u4e9f\u5f85\u4e3a\u62d3\u6251\u5b66\u6ce8\u5165\u65b0\u7684\u601d\u60f3\u3002<\/span><\/section>\n
    \n
  • \n
    Henri Poincar\u00e9 \u6d41\u5f62\u7684\u7ec4\u5408\u4e0d\u53d8\u91cf<\/span><\/section>\n<\/li>\n
  • \n
    Emmy Noether & Heinz Hopf \u628a\u7ec4\u5408\u62d3\u6251\u5b66\u5efa\u7acb\u5728\u65b0\u5174\u7684\u7fa4\u8bba\u4e0a\uff1a\u540c\u8c03\u7fa4<\/span><\/section>\n<\/li>\n
  • \n
    Henri Poincar\u00e9 & Heinz Hopf \u57fa\u672c\u7fa4\u3001\u540c\u4f26\u7406\u8bba<\/span><\/section>\n<\/li>\n
  • \n
    Henri Cartan & Samuel Eilenberg \u540c\u8c03\u4ee3\u6570\u3001\u6a21\u8303\u7574\u3001\u5bfc\u51fa\u51fd\u5b50<\/span><\/section>\n<\/li>\n
  • \n

    Samuel Eilenberg & Saunders Mac Lane \u62d3\u6251\u4e2d\u7684\u540c\u8c03\u7406\u8bba\u7528\u4e8e\u7fa4\u4e0a\u540c\u8c03<\/span><\/p>\n<\/li>\n<\/ul>\n


    <\/span><\/p>\n

    Saunders Mac Lane\u5c06\u8fd9\u4e9b\u5de5\u4f5c\u6574\u5408\u4e3a\u8303\u7574\u8bba\uff0c\u8bb8\u591a\u540d\u5bb6\u5728\u81ea\u5df1\u7684\u9886\u57df\u7528\u8303\u7574\u8bba\u7684\u65b9\u6cd5\u5f00\u62d3\u7586\u571f\uff0c\u53cd\u8fc7\u6765\u53c8\u4fc3\u8fdb\u4e86\u8303\u7574\u8bba\u7684\u53d1\u5c55\u3002<\/span><\/section>\n
      \n
    • \n
      Nobuo Yoneda \u7c73\u7530\u4fe1\u592b\uff1a\u7c73\u7530\u5f15\u7406<\/span><\/section>\n<\/li>\n
    • \n
      Alexander Grothendieck \u5728\u4ee3\u6570\u51e0\u4f55\u4e2d\u7cfb\u7edf\u53d1\u5c55\u4e86Abel\u8303\u7574\u548c\u5c42\u4e0a\u540c\u8c03\u3001topos\u7406\u8bba\u3001Grothendieck\u62d3\u6251<\/span><\/section>\n<\/li>\n
    • \n
      Daniel Kan \u6269\u5f20<\/span><\/section>\n<\/li>\n
    • \n
      Jean Leray \u5c42\u7406\u8bba<\/span><\/section>\n<\/li>\n
    • \n
      Daniel Quillen \u540c\u4f26\u7406\u8bba<\/span><\/section>\n<\/li>\n
    • \n

      William Lawvere \u8303\u7574\u5316\u7684\u903b\u8f91\u3001topos\u7406\u8bba\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n


      <\/span><\/p>\n

      \u5982\u4eca\uff0c\u5f53\u4ee3\u8303\u7574\u8bba\u7814\u7a76\u904d\u5730\u5f00\u82b1\u3002<\/span><\/p>\n


      <\/span><\/h2>\n


      <\/span><\/p>\n

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      <\/section>\n

      <\/section>\n
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      <\/svg><\/section>\n<\/section>\n<\/section>\n
      \n

      \u8303\u7574\u8bba\u76ee\u524d\u7684\u7814\u7a76\u72b6\u51b5\u53ca\u6f5c\u5728\u5e94\u7528\u65b9\u5411<\/strong><\/strong><\/p>\n<\/section>\n

      \n

      <\/section>\n

      <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


      <\/p>\n

      <\/span><\/h2>\n
        \n
      • \n
        Jacob Lurie\uff1a\u9ad8\u9636topos<\/span><\/section>\n<\/li>\n
      • \n
        Emily Riehl\uff1a\u65e0\u7a77\u8303\u7574<\/span><\/section>\n<\/li>\n
      • \n
        John Baez\uff1a\u62d3\u6251\u91cf\u5b50\u573a\u8bba<\/span><\/section>\n<\/li>\n
      • \n
        Guerino Mazzola\uff1a\u7528\u8303\u7574\u8bba\u7814\u7a76\u97f3\u4e50\u5b66<\/span><\/section>\n<\/li>\n
      • \n
        Bartosz Milewski\uff1a\u51fd\u6570\u5f0f\u7f16\u7a0b<\/span><\/section>\n<\/li>\n
      • \n

        David Spivak\uff1a\u8303\u7574\u5316\u7684\u5efa\u6a21\u65b9\u6cd5<\/span><\/p>\n<\/li>\n<\/ul>\n

        <\/span><\/p>\n

        \u6570\u5341\u5e74\u524d\uff0c\u8303\u7574\u8bba\u5728\u4ee3\u6570\u5b66\u5bb6\u548c\u62d3\u6251\u5b66\u5bb6\u7684\u5c0f\u5708\u5b50\u91cc\uff0c\u4e5f\u6709\u201c\u62bd\u8c61\u7684\u5e9f\u8bdd(abstract nonsense)\u201d\u7684\u201c\u58f0\u8a89\u201d\u3002Mac Lane \u7ecf\u5178\u7684\u8303\u7574\u8bba\u6559\u6750 Categories for the Working Mathematician<\/span> (GTM\u7cfb\u5217\uff0c\u6570\u5b66\u5de5\u4f5c\u8005\u5fc5\u77e5\u7684\u8303\u7574\u5b66\uff0c\u4e16\u754c\u56fe\u4e66\u51fa\u7248\u516c\u53f8\u6709\u5f71\u5370\u7248) <\/span>\uff0c\u66f4\u88ab\u9ed1\u4e3a\u201c\u4ee3\u6570\u5b66\u5bb6\u7684\u8303\u7574\u5b66\u201d\uff0c\u8a00\u4e0b\u4e4b\u610f\u5176\u62bd\u8c61\u7a0b\u5ea6\u4e5f\u53ea\u6709\u6570\u5b66\u9886\u57df\u6700\u62bd\u8c61\u7684\u4ee3\u6570\u5b66\u5bb6\u624d\u80fd\u5b66\u4f1a\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u6570\u5341\u5e74\u540e\uff0c\u65b0\u9896\u7684\u6570\u5b66\u6559\u6750\u548c\u4e13\u8457\uff0c\u7eb7\u7eb7\u4ee5\u8303\u7574\u8bba\u66ff\u4ee3\u96c6\u5408\u8bba\uff0c\u4f5c\u4e3a\u5efa\u7acb\u9886\u57df\u77e5\u8bc6\u4f53\u7cfb\u7684\u57fa\u7840\u3002\u8bb8\u591a\u6570\u5b66\u754c\u7684\u7814\u7a76\u4eba\u5458\u653e\u4e0b\u4e86\u5386\u53f2\u5305\u88b1\uff0c\u613f\u610f\u5728\u81ea\u5df1\u7684\u7814\u7a76\u9886\u57df\u4f53\u4f1a\u8303\u7574\u8bba\u7684\u601d\u60f3\uff0c\u5728\u4ee3\u6570\u51e0\u4f55\u3001\u6570\u8bba\u3001\u4e43\u81f3\u5206\u6790\u7b49\u65b9\u9762\u5f00\u62d3\u7586\u571f\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u7269\u7406\u5b66\u5bb6\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u3001\u8bed\u8a00\u5b66\u5bb6\u3001\u7cfb\u7edf\u5b66\u5bb6\u7b49\u4e5f\u7eb7\u7eb7\u6295\u5165\u8303\u7574\u8bba\u5728\u5404\u81ea\u9886\u57df\u7684\u5e94\u7528\u4e2d\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u5982\u4eca\uff0c\u8303\u7574\u8bba\u65e9\u5df2\u4e0d\u662f\u5916\u754c\u6240\u8ba4\u4e3a\u7684\u5e26\u6709\u795e\u79d8\u8272\u5f69\u7684\u667a\u529b\u6e38\u620f\u3002\u5728\u8ba1\u7b97\u673a\u9886\u57df\uff0c\u7f16\u7a0b\u4e2d\u7684\u51fd\u6570\u95ee\u9898\u88ab\u5de7\u5999\u5730\u8f6c\u5316\u4e3a\u8303\u7574\u8bba\u4e2d\u7684\u6001\u5c04\u95ee\u9898\uff0c\u8ba8\u8bba\u7f16\u7a0b\u5982\u540c\u8ba8\u8bba\u4e00\u4e2a\u96c6\u5408\u4e0a\u7684\u6620\u5c04\u3002\u7528\u8303\u7574\u8bba\u7684\u601d\u60f3\u5ba1\u89c6\u4e0a\u4e16\u7eaa 50 \u5e74\u4ee3\u7684 LISP\uff0c\u4ee5\u53ca\u66f4\u65e9\u7684 30 \u5e74\u4ee3 Alonzo Church \u63d0\u51fa\u7684 lambda \u6f14\u7b97\u3001Alan Turing \u7684\u8ba1\u7b97\u7406\u8bba\uff0c\u63a8\u52a8\u4e86\u51fd\u6570\u5f0f\u7f16\u7a0b<\/span> (functional programming) <\/span>\u7684\u9769\u547d\uff0c\u65b0\u7684\u51fd\u6570\u5f0f\u7f16\u7a0b\u7684\u601d\u60f3\u5728\u6700\u8fd1\u51e0\u5e74\u5e7f\u6cdb\u5730\u4f53\u73b0\u5728\u6d41\u884c\u7684JS\u3001Java\u3001Python\u3001C# \u7b49\u8bed\u8a00\u7684\u65b0\u7248\u672c\u4e2d\uff0c\u8bb8\u591a\u65b0\u751f\u7684\u5de5\u5177\u5927\u5e45\u5ea6\u964d\u4f4e\u4e86\u5f00\u53d1\u7684\u5197\u4f59\u5ea6\u3001\u7b80\u5316\u4e86\u8ba1\u7b97\u7cfb\u7edf\u7684\u89c4\u6a21\uff0c\u8fd9\u4e9b\u5de5\u5177\u80cc\u540e\u90fd\u6709\u8303\u7574\u8bba\u7684\u6307\u5bfc\u601d\u60f3\u3002<\/span><\/p>\n


        <\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \n
        \n
        \n

        <\/section>\n

        <\/section>\n
        \n
        <\/svg><\/section>\n<\/section>\n<\/section>\n
        \n

        \u8bfe\u7a0b\u5b89\u6392<\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/section>\n

        <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/p>\n

        \u6211\u4eec\u7684\u96c6\u667a\u8303\u7574\u8bba\u7cfb\u5217\u8bfe\u7a0b\u6682\u5b9a\u4e3a\u4e24\u5b63\u3002\u73b0\u5728\u542f\u52a8\u7684\u662f\u7b2c\u4e00\u5b63\u8bfe\u7a0b\uff0c\u9996\u6b21\u4e0a\u7ebf 4 \u8282\u8bfe\u7a0b\uff0c\u540e\u7eed\u6bcf\u5468\u66f4\u65b0\u4e00\u8282\uff0c\u76f4\u81f3\u66f4\u65b0\u5b8c\u6bd5\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u4e3a\u4e86\u9002\u5e94\u5e7f\u5927\u975e\u6570\u5b66\u4e13\u4e1a\u7231\u597d\u8005\u7684\u9700\u8981\uff0c\u7b2c\u4e00\u5b63\u5c3d\u91cf\u4ece\u8f83\u4f4e\u7684\u8d77\u70b9\u51fa\u53d1\uff0c\u5728\u8865\u5145\u5177\u4f53\u7684\u6570\u5b66\u77e5\u8bc6\u8fc7\u7a0b\u4e2d\uff0c\u8ba9\u5b66\u5458\u719f\u6089\u8303\u7574\u5316\u7684\u601d\u7ef4\u65b9\u5f0f\uff0c\u4e3a\u7406\u89e3\u62bd\u8c61\u7684\u8303\u7574\u8bba\u6982\u5ff5\u79ef\u7d2f\u5b9e\u4f8b\u3002\u7b2c\u4e00\u5b63\u5b8c\u6210\u540e\uff0c\u5b66\u5458\u5c06\u80fd\u591f\u4e86\u89e3\u8303\u7574\u8bba\u7684\u57fa\u672c\u77e5\u8bc6\uff0c\u5305\u62ec\u8303\u7574\u3001\u51fd\u5b50\u3001\u5bf9\u5076\u3001\u6781\u9650\uff0c\u5e76\u4e14\u5728\u4ee3\u6570\u3001\u62d3\u6251\u7b49\u65b9\u9762\u6709\u8303\u7574\u8bba\u89d2\u5ea6\u7684\u7406\u89e3\u3002\u7b2c\u4e8c\u5b63\u5219\u5728\u524d\u9762\u7684\u57fa\u7840\u4e0a\uff0c\u66f4\u52a0\u4fa7\u91cd\u7528\u4e13\u4e1a\u7684\u65b9\u5f0f\u5c55\u5f00\u66f4\u9ad8\u5c42\u6b21\u7684\u8303\u7574\u8bba\u77e5\u8bc6\u3002\u7b2c\u4e8c\u5b63\u5b8c\u6210\u540e\uff0c\u5b66\u5458\u5c06\u80fd\u591f\u4e86\u89e3\u8303\u7574\u8bba\u4e2d\u7684\u51fd\u5b50\u8303\u7574\u3001\u53ef\u8868\u51fd\u5b50\u3001\u4f34\u968f\u51fd\u5b50\u7b49\u8f83\u4e3a\u62bd\u8c61\u7684\u6982\u5ff5\uff0c\u5e76\u4e14\u80fd\u591f\u719f\u6089\u5f20\u91cf\u3001\u540c\u8c03\u3001\u5c42\u7b49\u6982\u5ff5\u7684\u8303\u7574\u5316\u8868\u8ff0\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u5b8c\u6210\u672c\u8bfe\u7a0b\uff0c\u53ef\u4ee5\u6ca1\u6709\u969c\u788d\u5730\u4e86\u89e3\u73b0\u4ee3\u4ee3\u6570\u3001\u62d3\u6251\u3001\u8303\u7574\u7b49\u9886\u57df\u7684\u8bb8\u591a\u57fa\u672c\u6982\u5ff5\uff0c\u4e3a\u8fdb\u4e00\u6b65\u7684\u5b66\u4e60\u548c\u7ed3\u5408\u81ea\u6211\u5174\u8da3\u7684\u7814\u7a76\u6253\u4e0b\u57fa\u7840\u3002\u66f4\u91cd\u8981\u7684\u662f\u53ef\u4ee5\u7406\u89e3\u8303\u7574\u8bba\u7684\u601d\u7ef4\u65b9\u5f0f\uff0c\u638c\u63e1\u521b\u65b0\u7684\u5de5\u5177\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \u901a\u884c\u7684\u8303\u7574\u8bba\u6559\u5b66\u65b9\u5f0f\u662f\u9762\u5411\u6570\u5b66\u4e13\u4e1a\u9ad8\u5e74\u7ea7\u672c\u79d1\u751f\u3001\u7814\u7a76\u6240\u548c\u79d1\u7814\u4eba\u5458\u7684\uff0c\u5165\u624b\u7684\u95e8\u69db\u8f83\u9ad8\u3002\u8003\u8651\u5230\u8303\u7574\u8bba\u7231\u597d\u8005\u7684\u8d77\u70b9\uff0c\u6211\u4eec\u91c7\u7528\u4e86\u4e0d\u4e00\u6837\u7684\u6559\u5b66\u65b9\u6848\u3002\u5728\u7b2c\u4e00\u5b63\u4e2d\uff0c\u6700\u521d\uff0c\u6211\u4eec\u4f1a\u5728\u96c6\u5408\u548c\u7ebf\u6027\u4ee3\u6570\u8fd9\u4e24\u4e2a\u5206\u652f\u4e2d\u63d0\u53d6\u7c7b\u4f3c\u7684\u95ee\u9898\uff0c\u7528\u8303\u7574\u8bba\u6765\u7ed9\u51fa\u7edf\u4e00\u7684\u63cf\u8ff0\uff0c\u8ba9\u5b66\u5458\u611f\u53d7\u5230\u8303\u7574\u8bba\u7684\u601d\u7ef4\u65b9\u5f0f\u548c\u62bd\u8c61\u80fd\u529b\uff08\u7b2c 1 \u8bfe\uff09\u3002\u4e4b\u540e\u6211\u4eec\u4f1a\u5c55\u5f00\u8bb2\u96c6\u5408\u76f8\u5173\u7684\u8303\u7574\u3001\u4ee3\u6570\u76f8\u5173\u7684\u8303\u7574\uff0c\u4e00\u8fb9\u4e86\u89e3\u8303\u7574\u8bba\u7684\u6982\u5ff5\uff0c\u4e00\u8fb9\u5728\u5177\u4f53\u7684\u6570\u5b66\u95ee\u9898\u4e2d\u79ef\u7d2f\u4f8b\u5b50\uff0c\u540c\u65f6\u638c\u63e1\u5177\u4f53\u7684\u4ee3\u6570\u7ed3\u6784\uff0c\u5982\u7fa4\u3001\u73af\u3001\u6a21\u3001\u7ebf\u6027\u7a7a\u95f4\u7b49\uff08\u7b2c2\u30013\u30014\u8bfe\uff09\u3002\u8fdb\u800c\u6211\u4eec\u4f1a\u7740\u91cd\u8c08\u7ebf\u6027\u7ed3\u6784\u4e2d\u4f53\u73b0\u7684\u8303\u7574\u3002\u77e9\u9635\u662f\u5929\u751f\u5177\u6709\u884c\u5217\u5bf9\u5076\u6027\u7684\u6570\u5b66\u7ed3\u6784\uff0c\u8ba8\u8bba\u77e9\u9635\u53ef\u4ee5\u81ea\u7136\u5730\u5f15\u51fa\u8bb8\u591a\u8303\u7574\u8bba\u7684\u6982\u5ff5\uff08\u7b2c5\u30016\u30017\u30018\u8bfe\uff09\u3002\u6b64\u5916\u6211\u4eec\u8fd8\u4f1a\u5728\u96c6\u5408\u7684\u57fa\u7840\u4e0a\u5f15\u51fa\u62d3\u6251\uff0c\u5e76\u4e14\u7528\u8303\u7574\u7684\u65b9\u5f0f\u4ecb\u7ecd\u5982\u4f55\u5c06\u62d3\u6251\u8fd9\u6837\u7684\u51e0\u4f55\u95ee\u9898\u8f6c\u5316\u5230\u540c\u8c03\u7fa4\u8fd9\u6837\u7684\u4ee3\u6570\u8303\u7574\u53bb\u89e3\u51b3\uff08\u7b2c9\u300110\u300111\u300112\u8bfe\uff09\u3002<\/span><\/p>\n


        <\/span><\/p>\n

        \n
        \n
        \n

        \u7b2c\u4e00\u5b63\u8bfe\u7a0b\u5927\u7eb2<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

          \n
        1. \n

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

        2. \n

          \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

        5. \n

          \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

        7. \n

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

        8. \n

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

        9. \n

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

        10. \n

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

        11. \n

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

        12. \n

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


          <\/span><\/h3>\n
          \n
          \n
          \n

          \u7b2c\u4e8c\u5b63\u8bfe\u7a0b\u5927\u7eb2\uff08\u6682\u62df\uff09<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

            \n
          1. \n

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

          2. \n

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

          3. \n

            \u5c42\u2014\u2014\u51fd\u5b50\u5316\u5730\u6784\u9020\u51e0\u4f55\u5b66<\/span><\/p>\n<\/li>\n

          4. \n

            \u51fd\u5b50\u8303\u7574<\/span><\/p>\n<\/li>\n

          5. \n

            \u53ef\u8868\u51fd\u5b50<\/span><\/p>\n<\/li>\n

          6. \n

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

          7. \n

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

          8. \n

            Kan\u6269\u5f20<\/span><\/p>\n<\/li>\n

          9. \n

            Topos<\/span><\/p>\n<\/li>\n

          10. \n

            \u9ad8\u9636\u8303\u7574<\/span><\/p>\n<\/li>\n<\/ol>\n


            <\/h2>\n


            <\/p>\n

            \n
            \n
            \n
            \n
            \n

            <\/section>\n

            <\/section>\n
            \n
            <\/svg><\/section>\n<\/section>\n<\/section>\n
            \n

            \u96c6\u667a\u8303\u7574\u8bba\u8bfe\u7a0b\u8bb2\u5e08<\/strong><\/strong><\/p>\n<\/section>\n

            \n

            <\/section>\n

            <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


            <\/p>\n

            <\/p>\n

            J-CAT\u732b\u5708<\/span><\/p>\n


            <\/span><\/p>\n

            \u6559\u80b2\u6cd5\u5c1d\u8bd5\u8005\uff0c\u540c\u65f6\u7ed9\u5c0f\u5b66\u3001\u4e2d\u5b66\u3001\u5927\u5b66\u3001\u7814\u7a76\u751f\u3001\u79d1\u7814\u4eba\u5458\u6388\u8bfe\uff0c\u5bfb\u627e\u4ece\u57fa\u7840\u5230\u524d\u6cbf\u7684\u6700\u77ed\u8def\u5f84\u3002<\/span><\/p>\n


            <\/span><\/p>\n

            \u7814\u7a76\u5174\u8da3\u5305\u62ec\uff1a\u8303\u7574\u8bba\u3001\u52a8\u529b\u7cfb\u7edf\u3001\u4eba\u5de5\u667a\u80fd\u3002<\/span><\/p>\n


            <\/span><\/p>\n


            <\/span><\/p>\n

            \n
            \n
            \n
            \n
            \n

            <\/section>\n

            <\/section>\n
            \n
            <\/svg><\/section>\n<\/section>\n<\/section>\n
            \n

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

            \n

            <\/section>\n

            <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


            <\/p>\n

            \u4e3a\u521d\u5b66\u8005\uff0c\u7279\u522b\u662f\u975e\u6570\u5b66\u4e13\u4e1a\u80cc\u666f\u7684\u7cfb\u7edf\u3001\u4fe1\u606f\u7814\u7a76\u8005\u63d0\u4f9b\u4e00\u4e2a\u8d77\u70b9\u4f4e\u3001\u6c34\u5e73\u9ad8\u3001\u89c2\u70b9\u65b0\u7684\u8303\u7574\u8bba\u57fa\u7840\u8bfe\u7a0b\u3002<\/span><\/p>\n


            <\/span><\/h2>\n


            <\/span><\/p>\n

            \n
            \n
            \n
            \n
            \n

            <\/section>\n

            <\/section>\n
            \n
            <\/svg><\/section>\n<\/section>\n<\/section>\n
            \n

            \u8bfe\u7a0b\u9002\u7528\u5bf9\u8c61<\/strong><\/strong><\/p>\n<\/section>\n

            \n

            <\/section>\n

            <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


            <\/p>\n

            \u5982\u679c\u60a8\u6ee1\u8db3\u4ee5\u4e0b\u4efb\u610f\u6761\u4ef6\uff0c\u6b22\u8fce\u4f60\u52a0\u5165\u6211\u4eec\uff0c\u5b66\u4e60\u8303\u7574\u8bba\uff01<\/span><\/section>\n
              \n
            • \n
              \u5bf9\u73b0\u4ee3\u6570\u5b66\u4f53\u7cfb\u548c\u65b9\u6cd5\u8bba\u6709\u5174\u8da3<\/span><\/section>\n<\/li>\n
            • \n
              \u5177\u6709\u4e13\u4e1a\u7684\u6570\u5b66\u8bad\u7ec3\uff0c\u5e0c\u671b\u4e86\u89e3\u8303\u7574\u8bba\uff0c\u4ece\u65b0\u7684\u89d2\u5ea6\u7814\u7a76\u7684\u79d1\u7814\u5de5\u4f5c\u8005<\/span><\/section>\n<\/li>\n
            • \n
              \u6709\u9ad8\u7b49\u4ee3\u6570\/\u7ebf\u6027\u4ee3\u6570\u80cc\u666f\u7684\u5927\u5b66\u751f\u3001\u7814\u7a76\u751f\u3001\u79d1\u7814\u5de5\u4f5c\u8005<\/span><\/section>\n<\/li>\n
            • \n
              \u5e0c\u671b\u4e86\u89e3\u8303\u7574\u8bba\u7684\u601d\u7ef4\u65b9\u5f0f<\/span><\/section>\n<\/li>\n
            • \n

              \u6709\u5174\u8da3\u7684\u4e2d\u5b66\u751f<\/span><\/p>\n<\/li>\n<\/ul>\n


              <\/h2>\n


              <\/p>\n

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              <\/section>\n

              <\/section>\n
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              <\/svg><\/section>\n<\/section>\n<\/section>\n
              \n

              \u5bf9\u5b66\u5458\u7684\u57fa\u7840\u8981\u6c42<\/strong><\/strong><\/p>\n<\/section>\n

              \n

              <\/section>\n

              <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


              <\/p>\n

              \u672c\u8bfe\u7a0b\u65e8\u5728\u5c3d\u53ef\u80fd\u964d\u4f4e\u8303\u7574\u8bba\u7684\u5b66\u4e60\u8d77\u70b9\u3002<\/span><\/section>\n

              \u5b66\u5458\u53ea\u9700\u5bf9\u9ad8\u7b49\u4ee3\u6570\/\u7ebf\u6027\u4ee3\u6570\u4e2d\u7684\u7ebf\u6027\u7a7a\u95f4\u3001\u7ebf\u6027\u6620\u5c04\u3001\u77e9\u9635\u8fd0\u7b97\u6709\u57fa\u672c\u4e86\u89e3\uff0c\u901a\u8fc7\u8bfe\u7a0b\u7684\u5b66\u4e60\u5373\u53ef\u5165\u95e8\u8303\u7574\u8bba\u3002<\/span><\/p>\n


              <\/span><\/h2>\n


              <\/span><\/p>\n

              \n
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              <\/section>\n

              <\/section>\n
              \n
              <\/svg><\/section>\n<\/section>\n<\/section>\n
              \n

              \u8303\u7574\u8bba\u76f8\u5173\u53c2\u8003\u8d44\u6599<\/strong><\/strong><\/p>\n<\/section>\n

              \n

              <\/section>\n

              <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


              <\/p>\n

              \n
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              \u53c2\u8003\u4e66\u7c4d<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

              \n


              <\/p>\n<\/section>\n

              \u8303\u7574\u8bba\u662f\u65b0\u751f\u7684\u524d\u6cbf\u6570\u5b66\u3002<\/span>\u6570\u5341\u5e74\u524d\u7684\u6570\u5b66\u4e13\u8457\u5f80\u5f80\u4ece\u96c6\u5408\u5f00\u59cb\u5c55\u5f00\uff0c\u800c\u73b0\u5728\u7684\u8d8b\u52bf\u662f\u8bb8\u591a\u6570\u5b66\u9886\u57df\u90fd\u662f\u4ece\u8303\u7574\u4f5c\u4e3a\u8d77\u6b65\u7684\u7ae0\u8282\u3002<\/span>\u9057\u61be\u7684\u662f\uff0c<\/span>\u76ee\u524d\u4e3a\u6b62\u5e76\u6ca1\u6709\u4e2d\u6587\u65b9\u9762\u4f18\u79c0\u7684\u8303\u7574\u8bba\u6559\u6750\u6216\u4e13\u8457<\/span>\u3002<\/span><\/p>\n

              \u4e0b\u9762\u5217\u51fa\u7684\u53c2\u8003\u4e66\u7c4d\u5bf9\u4e8e\u975e\u6570\u5b66\u4e13\u4e1a\u4eba\u58eb\u800c\u8a00\u5747\u6709\u4e00\u5b9a\u7684\u95e8\u69db\u3002\u6211\u4eec\u5217\u4e3e\u8fd9\u4e9b\u4e66\u7c4d\u662f\u4e3a\u4e86\u65b9\u4fbf\u5ef6\u4f38\u5230\u5177\u4f53\u7684\u6570\u5b66\u9886\u57df\uff0c\u4f46\u4e0d\u4e3b\u5f20\u76f4\u63a5\u4ee5\u8fd9\u4e9b\u4e66\u7c4d\u81ea\u5b66\uff0c\u8fd9\u4e9b\u4e66\u7c4d\u4e5f\u5e76\u975e\u672c\u8bfe\u7a0b\u5b66\u4e60\u6240\u5fc5\u9700\u7684\u3002\u901a\u8fc7\u672c\u7cfb\u5217\u7684\u8bfe\u7a0b\uff0c\u4ece\u6bd4\u8f83\u4f4e\u7684\u8d77\u70b9\u5b8c\u6210\u4e86\u8303\u7574\u8bba\u7684\u5165\u95e8\u73af\u8282\u540e\uff0c\u518d\u6839\u636e\u81ea\u8eab\u5174\u8da3\u7814\u4e60\u4f1a\u6709\u4e8b\u534a\u529f\u500d\u7684\u6548\u679c\u3002\u5c4a\u65f6\u518d\u770b\u8fd9\u4e9b\u4e66\u7c4d\uff0c\u5982\u679c\u6709\u8c41\u7136\u5f00\u6717\u7684\u611f\u89c9\uff0c\u4fbf\u4f53\u73b0\u4e86\u672c\u8bfe\u7a0b\u7684\u5b97\u65e8\u3002<\/span><\/section>\n