{"id":29296,"date":"2021-10-12T14:49:11","date_gmt":"2021-10-12T06:49:11","guid":{"rendered":"https:\/\/swarma.org\/?p=29296"},"modified":"2021-10-12T14:49:11","modified_gmt":"2021-10-12T06:49:11","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%e7%ac%ac%e4%ba%8c%e5%ad%a3-%e8%b7%a8%e5%ad%a6%e7%a7%91%e7%9a%84%e7%a7%91%e5%ad%a6%e6%96%b9%e6%b3%95%e8%ae%ba","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=29296","title":{"rendered":"\u4eba\u4eba\u53ef\u5b66\u7684\u8303\u7574\u8bba\u7b2c\u4e8c\u5b63\u2014\u2014\u8de8\u5b66\u79d1\u7684\u79d1\u5b66\u65b9\u6cd5\u8bba | \u7cbe\u54c1\u5165\u95e8\u7cfb\u5217\u8bfe"},"content":{"rendered":"
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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><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n

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\u5728\u5f53\u4ee3\u6570\u5b66\u6839\u6df1\u53f6\u8302\u7684\u4f53\u7cfb\u4e2d\uff0c\u8303\u7574\u8bba\u662f\u6700\u5e74\u8f7b\u3001\u6700\u62bd\u8c61\u3001\u79bb\u751f\u6d3b\u6700\u8fdc\u7684\u5206\u652f\uff0c\u5230\u5982\u4eca\u5df2\u7ecf\u53d1\u5c55\u4e86\u6570\u5341\u5e74\uff0c\u5176\u5f71\u54cd\u6ce2\u53ca\u8bb8\u591a\u9886\u57df\u3002\u8303\u7574\u8bba\u4e0d\u4ec5\u65e9\u5df2\u6446\u8131\u5728\u53d1\u5c55\u521d\u671f\u8fde\u6570\u5b66\u5de5\u4f5c\u8005\u90fd\u8ba4\u4e3a\u662f\u201c\u62bd\u8c61\u7684\u5e9f\u8bdd<\/span>(abstract nonsense)<\/span>\u201d\u7684\u5f62\u8c61\uff0c\u5982\u4eca\u53cd\u800c\u4e0d\u65ad\u6e17\u900f\u5230\u6570\u5b66\u7684\u5404\u5927\u5206\u652f\uff0c\u5f71\u54cd\u5230\u7269\u7406\u3001\u4fe1\u606f\u3001\u751f\u547d\u79d1\u5b66\u3001\u793e\u4f1a\u79d1\u5b66\u3001\u54f2\u5b66\u7b49\u8bf8\u591a\u9886\u57df\uff0c\u5927\u6709\u4e00\u7edf\u6c5f\u6e56\u7684\u52bf\u5934\u3002<\/span><\/section>\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<\/strong>\u4e0a\u4e16\u7eaa\u521d\u51e0\u4f55\u5b66\u7684\u53d1\u5c55\u4e9f\u5f85\u4e3a\u62d3\u6251\u5b66\u6ce8\u5165\u65b0\u7684\u601d\u60f3\uff0c\u8303\u7574\u8bba\u6210\u4e3a\u7814\u7a76\u62d3\u6251\u5b66\u3001\u4ee3\u6570\u5b66\u3001\u6570\u8bba\u7b49\u4e0d\u53ef\u7f3a\u5c11\u7684\u5de5\u5177\u3002\u6570\u5b66\u5bb6\u4eec\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

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\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<\/span>(abstract nonsense)<\/span>\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><\/section>\n

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\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><\/section>\n

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\u6211\u4eec\u600e\u4e48\u8bb2\u6388\u8303\u7574\u8bba<\/strong><\/strong><\/p>\n<\/section>\n

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<\/h3>\n
\u8bb8\u591a\u504f\u7406\u8bba\u7684\u6587\u732e\u5f80\u5f80\u4ee5\u96c6\u5408\u8bba\u7684\u7ae0\u8282\u4f5c\u4e3a\u5f00\u7bc7\u7684\u9884\u5907\u77e5\u8bc6\u3002\u800c\u5f53\u4ee3\u524d\u6cbf\u7684\u7814\u7a76\u6587\u732e\uff0c\u8d8a\u6765\u8d8a\u591a\u4ee5\u8303\u7574\u8bba\u4f5c\u4e3a\u5f00\u573a\u767d\uff0c\u8303\u7574\u8bba\u5df2\u7ecf\u6210\u4e3a\u4e00\u79cd\u65b9\u4fbf\u7684\u63cf\u8ff0\u8bed\u8a00\u3002\u7ecf\u8fc7\u8303\u7574\u8bba\u7b2c\u4e00\u5b63\u548c\u7b2c\u4e8c\u5b63\u7684\u8bfe\u7a0b\u5b66\u4e60\uff0c\u4f60\u5c06\u5bf9\u8303\u7574\u8bba\u7684\u63cf\u8ff0\u65b9\u5f0f\u4e0d\u518d\u964c\u751f\uff0c\u53ef\u4ee5\u76f4\u63a5\u8fdb\u5165\u76f8\u5173\u7684\u7814\u7a76\u4e3b\u9898\u3002<\/span><\/section>\n

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\u5982\u679c\u4f60\u6709\u6570\u5b66\u4e13\u4e1a\u80cc\u666f\uff0c\u5728\u7b2c\u4e00\u5b63\u4e2d\u770b\u5230\u7684\u90fd\u662f\u719f\u6089\u7684\u77e5\u8bc6\uff1a\u7fa4\u3001\u73af\u3001\u6a21\u3001\u7ebf\u6027\u7a7a\u95f4\u3001\u62d3\u6251\u2026\u2026\u7136\u800c\uff0c\u5728\u6211\u4eec\u7684\u8bfe\u7a0b\u4e2d\uff0c\u91c7\u7528\u4e86\u8303\u7574\u8bba\u7684\u8bed\u8a00\u5bf9\u5176\u8fdb\u884c\u4e86\u518d\u53d9\u8ff0\uff0c\u7528\u8303\u7574\u7684\u89d2\u5ea6\u6765\u770b\u5f85\u719f\u77e5\u7684\u95ee\u9898\uff0c\u611f\u53d7\u8303\u7574\u8bba\u7684\u601d\u7ef4\u65b9\u5f0f\u3002\u5728\u719f\u6089\u57fa\u672c\u7684\u8303\u7574\u8bba\u8bed\u8a00\u540e\uff0c\u5373\u4fbf\u5728\u4ee3\u6570\u62d3\u6251\u3001\u4ee3\u6570\u51e0\u4f55\u4e2d\u9047\u5230\u8303\u7574\u5316\u7684\u63cf\u8ff0\uff0c\u4e5f\u4e0d\u4f1a\u6210\u4e3a\u5b66\u4e60\u7684\u969c\u788d\u3002<\/span><\/section>\n

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\u603b\u7684\u6765\u8bf4\uff0c\u7b2c\u4e00\u5b63\u8bfe\u7a0b\u7684\u4e3b\u8981\u76ee\u7684\u662f\u4e3a\u4e86\u8ba9\u5b66\u5458\u80fd\u591f\u770b\u61c2\u4e00\u4e9b\u8303\u7574\u8bba\u4e2d\u5e38\u89c1\u7684\u4f8b\u5b50\uff0c\u8fd9\u6837\u624d\u80fd\u4ece\u4f8b\u5b50\u4e2d\uff0c\u5b66\u4e60\u62bd\u8c61\u7684\u8303\u7574\u8bba\u77e5\u8bc6\u3002\u6211\u4eec\u5df2\u7ecf\u4e60\u60ef\u4e8e\u628a\u5404\u79cd\u5177\u4f53\u7684\u95ee\u9898\u8f6c\u5316\u4e3a\u8303\u7574\u7684\u95ee\u9898\u2014\u2014\u4e00\u5207\u95ee\u9898\u90fd\u662f\u7bad\u5934\u7684\u95ee\u9898\u3002\u5728\u5404\u79cd\u7bad\u5934\u4e4b\u95f4\u8fdb\u884c\u62bd\u8c61\u7684\u7814\u7a76\uff0c\u5e76\u975e\u662f\u4e00\u79cd\u62bd\u8c61\u5e9f\u8bdd\u7684\u667a\u529b\u6e38\u620f\uff0c\u800c\u662f\u5bf9\u73b0\u5b9e\u95ee\u9898\u7684\u9ad8\u5ea6\u62bd\u8c61\u548c\u5e7f\u6cdb\u8054\u7cfb\u3002<\/strong><\/span><\/section>\n

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\u4e60\u5f97\u8fd9\u79cd\u601d\u7ef4\u65b9\u5f0f\u540e\uff0c\u8303\u7574\u8bba\u7b2c\u4e8c\u5b63\u7684\u8bfe\u7a0b\u5c06\u7ad9\u5728\u4e00\u4e2a\u65b0\u7684\u8d77\u70b9\u4e0a\uff0c\u4f1a\u66f4\u591a\u5173\u6ce8\u8303\u7574\u8bba\u5185\u5728\u7684\u95ee\u9898\u3002\u5bf9\u62bd\u8c61\u7684\u7bad\u5934\u672c\u8eab\u7684\u7814\u7a76\uff0c\u901a\u5e38\u6d89\u53ca\u5230\u8303\u7574\u8bba\u7814\u7a76\u7684\u4e3b\u8981\u8bdd\u9898\uff0c\u5982\u51fd\u5b50\u8303\u7574\u30012-\u8303\u7574\u3001\u81ea\u7136\u53d8\u6362\u3001\u53ef\u8868\u51fd\u5b50\u3001Yoneda\u5f15\u7406\u3001\u6cdb\u6027\u8d28\u3001\u4f34\u968f\u51fd\u5b50\u3001\u5355\u5b50\u7b49\u7b49\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7b2c\u4e00\u5b63\u8bfe\u7a0b\u4ece\u7ebf\u6027\u4ee3\u6570\u5165\u95e8\uff0c\u81ea\u7136\u7b2c\u4e8c\u5b63\u4e2d\u4e5f\u4f1a\u4ece\u7ebf\u6027\u4ee3\u6570\u5c55\u5f00\u5f20\u91cf\u7684\u6982\u5ff5\uff0c\u4ece\u7ebf\u6027\u7a7a\u95f4\u7684\u5f20\u91cf\uff0c\u5230\u6a21\u7684\u5f20\u91cf\u3001\u5f20\u91cf\u4ee3\u6570\uff0c\u4ee5\u53ca\u8303\u7574\u8bba\u4e2d\u7684 Abel \u8303\u7574\u548c\u5e7a\u534a\u8303\u7574\u3002\u7b2c\u4e8c\u5b63\u7684\u5185\u5bb9\u57fa\u672c\u4e0a\u6d89\u53ca\u5230\u4e86\u901a\u5e38\u8303\u7574\u8bba\u6559\u7a0b\u7684\u4e3b\u8981\u5185\u5bb9\uff0c\u5305\u62ec\u62d3\u6251\u3001\u4ee3\u6570\u51e0\u4f55\u3001\u91cf\u5b50\u7269\u7406\u3001\u91cf\u5b50\u4fe1\u606f\u7b49\u8303\u7574\u8bba\u5e94\u7528\u8f83\u6df1\u5165\u7684\u65b9\u5411\uff0c\u7b2c\u4e8c\u5b63\u5b66\u5230\u7684\u77e5\u8bc6\u548c\u601d\u7ef4\u65b9\u5f0f\uff0c\u53ef\u4ee5\u76f4\u63a5\u5e2e\u52a9\u4f60\u8d70\u5230\u7814\u7a76\u524d\u6cbf\u3002<\/span><\/section>\n

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\u8bfe\u7a0b\u4ecb\u7ecd<\/strong><\/strong><\/p>\n<\/section>\n

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


<\/p>\n

<\/h3>\n

\u8bfe\u7a0b\u5927\u7eb2\uff08\u7b2c\u4e8c\u5b63\uff09\uff08\u5f85\u5b9a\uff09<\/span><\/strong><\/span><\/h4>\n
    \n
  1. \n
    \u7528\u7bad\u5934\u6784\u9020\u77e9\u9635\uff08\u514d\u8d39\u516c\u5f00\uff09<\/span><\/section>\n<\/li>\n
  2. \n
    \u51fd\u5b50\u8303\u7574\uff08\u514d\u8d39\u516c\u5f00\uff09<\/span><\/section>\n<\/li>\n
  3. \n
    \u53ef\u8868\u51fd\u5b50I<\/span><\/section>\n<\/li>\n
  4. \n
    \u53ef\u8868\u51fd\u5b50II<\/span><\/section>\n<\/li>\n
  5. \n
    Yoneda\u5f15\u7406<\/span><\/section>\n<\/li>\n
  6. \n
    \u4f34\u968f\u51fd\u5b50<\/span><\/section>\n<\/li>\n
  7. \n
    \u5f20\u91cf\u79ef<\/span><\/section>\n<\/li>\n
  8. \n
    \u5f20\u91cf\u4ee3\u6570<\/span><\/section>\n<\/li>\n
  9. \n
    \u5e7a\u534a\u8303\u7574<\/span><\/section>\n<\/li>\n
  10. \n
    \u5355\u5b50<\/span><\/section>\n<\/li>\n
  11. \n
    \u6cdb\u6027\u8d28<\/span><\/section>\n<\/li>\n
  12. \n
    Abel\u8303\u7574<\/span><\/section>\n<\/li>\n<\/ol>\n


    <\/h4>\n

    \u8bfe\u7a0b\u8bb2\u5e08<\/span><\/strong><\/span><\/h4>\n
    \u672c\u5b63\u8bfe\u7a0b\u4ecd\u7531\u7b2c\u4e00\u5b63\u6388\u8bfe\u8001\u5e08J-CAT\u8bb2\u6388\u3002\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\u7814\u7a76\u5174\u8da3\u5305\u62ec\uff1a\u8303\u7574\u8bba\u3001\u52a8\u529b\u7cfb\u7edf\u3001\u4eba\u5de5\u667a\u80fd\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    <\/section>\n

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


    <\/h4>\n

    \u4f60\u5c06\u83b7\u5f97<\/strong><\/span><\/h4>\n
    \u8303\u7574\u8bba\u7b2c\u4e8c\u5b63\u8bfe\u7a0b\u9762\u5411\u5df2\u7ecf\u5177\u5907\u8303\u7574\u8bba\u57fa\u672c\u6982\u5ff5\u548c\u76f8\u5173\u6570\u5b66\u80cc\u666f<\/span>\uff08\u7b2c\u4e00\u5b63\u8bfe\u7a0b\u5927\u4f53\u6240\u8986\u76d6\u7684\u77e5\u8bc6\uff09<\/span>\uff0c\u671f\u671b\u8fdb\u4e00\u6b65\u5b66\u4e60\u8303\u7574\u8bba\u7684\u5b66\u5458\u3002<\/span><\/section>\n

    <\/span><\/section>\n
    \u7ecf\u8fc7\u672c\u5b63\u8bfe\u7a0b\u5b66\u4e60\uff0c\u5b66\u5458\u5c06\u521d\u6b65\u638c\u63e1\u51fd\u5b50\u8303\u7574\u30012-\u8303\u7574\u3001\u81ea\u7136\u53d8\u6362\u3001\u53ef\u8868\u51fd\u5b50\u3001Yoneda\u5f15\u7406\u3001\u6cdb\u6027\u8d28\u3001\u4f34\u968f\u51fd\u5b50\u3001\u5355\u5b50\u7b49\u91cd\u8981\u6982\u5ff5\u3002<\/span><\/section>\n

    <\/span><\/section>\n

    \u5b66\u4e60\u5efa\u8bae<\/span><\/strong><\/span><\/h4>\n
    \u96c6\u667a\u8303\u7574\u8bba\u5165\u95e8\u7cfb\u5217\u8bfe\u7a0b\u7b2c\u4e00\u5b63\u7684\u5b66\u5458\u4ece\u5728\u8bfb\u7684\u5927\u5b66\u751f\u3001\u5728\u804c\u7684\u6570\u5b66\u7231\u597d\u8005\u3001\u7814\u7a76\u751f\u3001\u6559\u5b66\u79d1\u7814\u4eba\u58eb\uff0c\u5230\u4e00\u4e2a\u7814\u7a76\u8bfe\u9898\u7ec4\u7684\u5e08\u751f\u3002\u4ed6\u4eec\u7684\u7814\u7a76\u5174\u8da3\u5305\u62ec\u6570\u5b66\u3001\u7269\u7406\u3001\u91cf\u5b50\u4fe1\u606f\u3001\u4eba\u5de5\u667a\u80fd\u3001\u8ba1\u7b97\u7406\u8bba\u3001\u751f\u547d\u79d1\u5b66\u3001\u7ecf\u6d4e\u5b66\u7b49\uff0c\u8fd9\u65e2\u4f53\u73b0\u4e86\u96c6\u667a\u793e\u533a\u6d3b\u8dc3\u7684\u4ea4\u53c9\u5b66\u79d1\u5b66\u4e60\u6c1b\u56f4\uff0c\u4e5f\u4f53\u73b0\u4e86\u8303\u7574\u8bba\u7b2c\u4e00\u5b63\u7684\u8bbe\u8ba1\u521d\u8877\uff0c\u6253\u9020\u4e00\u4e2a\u201c\u4eba\u4eba\u53ef\u5b66\u201d\u7684\u8303\u7574\u8bba\u5165\u95e8\u8bfe\u7a0b\u3002\u7b2c\u4e00\u5b63\u6536\u5230\u4e86\u5f88\u591a\u5b66\u5458\u79ef\u6781\u7684\u53cd\u9988\uff0c\u60f3\u542c\u542c\u5927\u5bb6\u600e\u4e48\u8bf4\uff0c\u53ef\u89c1\u6587\u7ae0\uff1a\u8303\u7574\u8bba\u4eba\u4eba\u7686\u53ef\u5165\u95e8\uff1f\u8001\u5e08\u548c\u540c\u5b66\u4eec\u8fd9\u6837\u8bf4\u2014\u2014<\/a><\/span><\/section>\n

    <\/span><\/section>\n
    \u5982\u679c\u60a8\u6ee1\u8db3\u4ee5\u4e0b\u4efb\u610f\u6761\u4ef6\uff0c\u4f46\u5c1a\u672a\u6709\u57fa\u7840\u7684\u8303\u7574\u8bba\u77e5\u8bc6\uff0c\u8bf7\u5148\u5b66\u4e60\u7b2c\u4e00\u5b63\u8bfe\u7a0b<\/strong>\uff1a<\/span><\/section>\n