[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki25\/archives\/291803#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki25\/archives\/291803","headline":"\u5f15\u304d\u623b\u3057 (\u570f\u8ad6) – Wikipedia","name":"\u5f15\u304d\u623b\u3057 (\u570f\u8ad6) – Wikipedia","description":"\u570f\u8ad6\u3068\u3044\u3046\u6570\u5b66\u306e\u5206\u91ce\u306b\u304a\u3044\u3066\uff0c\u5f15\u304d\u623b\u3057\uff08\u3072\u304d\u3082\u3069\u3057\uff0c\u82f1: pullback\uff09\uff0c\u3042\u308b\u3044\u306f\u30d5\u30a1\u30a4\u30d0\u30fc\u7a4d (fiber\/fibre\/fibered product)\uff0c\u30c7\u30ab\u30eb\u30c8\u306e\u56db\u89d2\u5f62 (Cartesian square) \u3068\u306f\uff0c\u5171\u901a\u306e\u7d42\u57df\u3092\u6301\u30642\u3064\u306e\u5c04 f: X \u2192 Z, g: Y \u2192 Z \u304b\u3089\u306a\u308b\u56f3\u5f0f\u306e\u6975\u9650\u3067\u3042\u308b\uff0e\u5f15\u304d\u623b\u3057\u306f\u3057\u3070\u3057\u3070 P = X \u00d7ZY","datePublished":"2022-04-26","dateModified":"2022-04-26","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki25\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki25\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/ab\/Categorical_pullback.svg\/125px-Categorical_pullback.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/ab\/Categorical_pullback.svg\/125px-Categorical_pullback.svg.png","height":"122","width":"125"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki25\/archives\/291803","about":["Wiki"],"wordCount":5120,"articleBody":"\u570f\u8ad6\u3068\u3044\u3046\u6570\u5b66\u306e\u5206\u91ce\u306b\u304a\u3044\u3066\uff0c\u5f15\u304d\u623b\u3057\uff08\u3072\u304d\u3082\u3069\u3057\uff0c\u82f1: pullback\uff09\uff0c\u3042\u308b\u3044\u306f\u30d5\u30a1\u30a4\u30d0\u30fc\u7a4d (fiber\/fibre\/fibered product)\uff0c\u30c7\u30ab\u30eb\u30c8\u306e\u56db\u89d2\u5f62 (Cartesian square) \u3068\u306f\uff0c\u5171\u901a\u306e\u7d42\u57df\u3092\u6301\u30642\u3064\u306e\u5c04 f: X \u2192 Z, g: Y \u2192 Z \u304b\u3089\u306a\u308b\u56f3\u5f0f\u306e\u6975\u9650\u3067\u3042\u308b\uff0e\u5f15\u304d\u623b\u3057\u306f\u3057\u3070\u3057\u3070P = X \u00d7ZY  \u3068\u66f8\u304b\u308c\uff0c2\u3064\u306e\u81ea\u7136\u306a\u5c04 P \u2192 X, P \u2192 Y \u3092\u5099\u3048\u3066\u3044\u308b\uff0e2\u3064\u306e\u5c04\u306e\u5f15\u304d\u623b\u3057\u304c\u5b58\u5728\u3059\u308b\u3068\u306f\u9650\u3089\u306a\u3044\u304c\uff0c\u5b58\u5728\u3059\u308c\u30702\u3064\u306e\u5c04\u304b\u3089\u672c\u8cea\u7684\u306b\u4e00\u610f\u306b\u5b9a\u7fa9\u3055\u308c\u308b\uff0e\u591a\u304f\u306e\u72b6\u6cc1\u306b\u304a\u3044\u3066\uff0cX \u00d7ZY \u306f\uff0c\u5143 x \u2208 X \u3068 y \u2208 Y \u306e\u5bfe (x, y) \u3067\u3042\u3063\u3066 f(x) = g(y) \u306a\u308b\u3082\u306e\u304b\u3089\u306a\u308b\u3082\u306e\u3068\u76f4\u89b3\u7684\u306b\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u4e00\u822c\u306e\u5b9a\u7fa9\u306b\u306f\u666e\u904d\u6027\u304c\u7528\u3044\u3089\u308c\uff0c\u3053\u306e\u3053\u3068\u3092\u672c\u8cea\u7684\u306a\u7406\u7531\u3068\u3057\u3066\uff0c\u5f15\u304d\u623b\u3057\u306f2\u3064\u306e\u4e0e\u3048\u3089\u308c\u305f\u5c04\u3092\u53ef\u63db\u56db\u89d2\u5f62\u306b\u9069\u5408\u3055\u305b\u308b\u300c\u6700\u3082\u4e00\u822c\u306e\u300d\u65b9\u6cd5\u3067\u3042\u308b\uff0e\u5f15\u304d\u623b\u3057\u306e\u53cc\u5bfe\u6982\u5ff5\u306f\u62bc\u3057\u51fa\u3057\uff08\u82f1\u8a9e\u7248\uff09 (pushout) \u3067\u3042\u308b\uff0e\u660e\u793a\u7684\u306b\u306f\uff0c2\u3064\u306e\u5c04 f, g \u306e\u5f15\u304d\u623b\u3057\u306f\uff0c\u5bfe\u8c61 P \u30682\u3064\u306e\u5c04 p1: P \u2192 X \u3068 p2: P \u2192 Y \u3067\u3042\u3063\u3066\u6b21\u306e\u56f3\u5f0f\u304c\u53ef\u63db\u3068\u306a\u308b\u3082\u306e\u304b\u3089\u306a\u308b\uff1a  \u3055\u3089\u306b\uff0c\u5f15\u304d\u623b\u3057 (P, p1, p2) \u306f\u3053\u306e\u56f3\u5f0f\u306b\u3064\u3044\u3066\u666e\u904d\u7684\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\uff0c\u3064\u307e\u308a\uff0c\u5225\u306e\u305d\u306e\u3088\u3046\u306a3\u3064\u7d44 (Q, q1, q2) \u3067\u3042\u3063\u3066\u6b21\u306e\u56f3\u5f0f\u304c\u53ef\u63db\u3067\u3042\u308b\u3088\u3046\u306a\u4efb\u610f\u306e\u3082\u306e\u306b\u5bfe\u3057\u3066\uff0c\u4e00\u610f\u7684\u306a u:\u00a0Q\u00a0\u2192\u00a0P\uff08\u4ef2\u4ecb\u5c04 (mediating morphism) \u3068\u547c\u3070\u308c\u308b\uff09\u304c\u5b58\u5728\u3057\u3066p2\u2218u=q2,p1\u2218u=q1{displaystyle p_{2}circ u=q_{2},qquad p_{1}circ u=q_{1}}\u3068\u306a\u3089\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\uff0e\u3059\u3079\u3066\u306e\u666e\u904d\u7684\u306a\u69cb\u6210\u304c\u305d\u3046\u3067\u3042\u308b\u3088\u3046\u306b\uff0c\u5f15\u304d\u623b\u3057\u306f\uff0c\u5b58\u5728\u3059\u308c\u3070\uff0c\u540c\u578b\u3092\u9664\u3044\u3066\u4e00\u610f\u3067\u3042\u308b\uff0e\u5b9f\u969b\uff0c\u540c\u3058 cospan\uff08\u82f1\u8a9e\u7248\uff09 X\u00a0\u2192\u00a0Z\u00a0\u2190\u00a0Y \u306e2\u3064\u306e\u5f15\u304d\u623b\u3057 (A, a1, a2) \u3068 (B, b1, b2) \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\uff0cA \u3068 B \u306e\u9593\u306e\u5f15\u304d\u623b\u3057\u69cb\u9020\u3092\u5c0a\u91cd\u3057\u305f\u4e00\u610f\u7684\u306a\u540c\u578b\u304c\u5b58\u5728\u3059\u308b\uff0e  Table of Contents\u5f31\u3044\u5f15\u304d\u623b\u3057[\u7de8\u96c6]\u5f15\u304d\u623b\u3057\u3068\u7a4d[\u7de8\u96c6]\u53ef\u63db\u74b0[\u7de8\u96c6]\u96c6\u5408[\u7de8\u96c6]\u30d5\u30a1\u30a4\u30d0\u30fc\u675f[\u7de8\u96c6]\u9006\u50cf\u3068\u5171\u901a\u90e8\u5206[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]\u5f31\u3044\u5f15\u304d\u623b\u3057[\u7de8\u96c6]\u4f59\u30b9\u30d1\u30f3X \u2192 Z \u2190 Y \u306e\u5f31\u5f15\u304d\u623b\u3057 (weak pullback) \u306f\u300c\u5f31\u3044\u666e\u904d\u6027\u300d\u3057\u304b\u6301\u305f\u306a\u3044\uff08\u3064\u307e\u308a\u3001\u4e0a\u8a18\u306e\u4ef2\u4ecb\u5c04 u: Q \u2192 P \u304c\u4e00\u610f\u3067\u3042\u308b\u3053\u3068\u3092\u8981\u6c42\u3057\u306a\u3044\uff09\u3088\u3046\u306a\u4f59\u30b9\u30d1\u30f3\u4e0a\u306e\u9310\u3092\u8a00\u3046\u3002[1]\u5f15\u304d\u623b\u3057\u3068\u7a4d[\u7de8\u96c6]\u5f15\u304d\u623b\u3057\u306f\u7a4d\u3068\u4f3c\u3066\u3044\u308b\u304c\uff0c\u540c\u3058\u3067\u306f\u306a\u3044\uff0e\u5c04 f, g \u3068\u5bfe\u8c61 Z \u306e\u5b58\u5728\u3092\u300c\u5fd8\u308c\u308b\u300d\u3053\u3068\u306b\u3088\u3063\u3066\u7a4d\u304c\u5f97\u3089\u308c\u308b\uff0e\u3053\u306e\u3068\u304d2\u3064\u306e\u5bfe\u8c61 X, Y \u306e\u307f\u3092\u6301\u3061\u305d\u308c\u3089\u306e\u9593\u306b\u4f55\u306e\u5c04\u3082\u306a\u3044\u96e2\u6563\u570f\u304c\u6b8b\u308b\u304c\uff0c\u3053\u306e\u96e2\u6563\u570f\u306f\u901a\u5e38\u306e\u4e8c\u9805\u7a4d\u3092\u69cb\u6210\u3059\u308b\u305f\u3081\u306e\u6dfb\u5b57\u96c6\u5408\u3068\u3057\u3066\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u3057\u305f\u304c\u3063\u3066\uff0c\u5f15\u304d\u623b\u3057\u306f\u4ed8\u52a0\u69cb\u9020\u3092\u6301\u3063\u305f\u901a\u5e38\u306e\uff08\u30c7\u30ab\u30eb\u30c8\uff09\u7a4d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0eZ, f, g \u3092\u300c\u5fd8\u308c\u308b\u300d\u4ee3\u308f\u308a\u306b\uff0c\u305d\u308c\u3089\u3092\u300c\u81ea\u660e\u5316\u300d\u3059\u308b\u3053\u3068\u3082 Z \u3092\u7d42\u5bfe\u8c61\uff08\u5b58\u5728\u306f\u4eee\u5b9a\u3059\u308b\uff09\u306b\u7279\u6b8a\u5316\u3059\u308c\u3070\u53ef\u80fd\u3067\uff08\u3053\u306e\u5834\u5408 f \u3068 g \u306f\u4e00\u610f\u306b\u6c7a\u307e\u3063\u3066\uff0c\u3057\u304b\u3082\u4f55\u306e\u60c5\u5831\u3082\u4e0e\u3048\u306a\u3044\uff09\uff0c\u3053\u306e cospan \u306e\u5f15\u304d\u623b\u3057\u306f X \u3068 Y \u306e\u7a4d\u3068\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u53ef\u63db\u74b0[\u7de8\u96c6]  \u53ef\u63db\u74b0\u306e\u570f\u306f\u5f15\u304d\u623b\u3057\u3092\u6301\u3064\uff0e\uff08\u5358\u4f4d\u5143\u3092\u6301\u3064\uff09\u53ef\u63db\u74b0\u306e\u570f CRing \u306b\u304a\u3044\u3066\uff0c\u5f15\u304d\u623b\u3057\u306f\u30d5\u30a1\u30a4\u30d0\u30fc\u7a4d\u3068\u547c\u3070\u308c\u308b\uff0eA, B, C \u2208 Ob(CRing),\u03b1\u00a0: A \u2192 C \u2208 Hom(CRing),\u03b2\u00a0: B \u2192 C \u2208 Hom(CRing)\u3068\u3059\u308b\uff0e\u3057\u305f\u304c\u3063\u3066 A, B, C \u306f\u5358\u4f4d\u5143\u3092\u6301\u3064\u53ef\u63db\u74b0\u3067\u3042\u308a\uff0c\u03b1, \u03b2 \u306f\u5358\u4f4d\u5143\u3092\u4fdd\u3064\u74b0\u6e96\u540c\u578b\u3067\u3042\u308b\uff0e\u3059\u308b\u3068\u3053\u306e\u56f3\u5f0f\u306e\u5f15\u304d\u623b\u3057\u306f\u30c7\u30ab\u30eb\u30c8\u7a4d A \u00d7 B \u306e\u90e8\u5206\u74b0A\u00d7CB={(a,b)\u2208A\u00d7B\u2223\u03b1(a)=\u03b2(b)}{displaystyle Atimes _{C}B={(a,b)in Atimes Bmid alpha (a)=beta (b)}}\u3068\u6b21\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u5c04\u03b2\u2032:A\u00d7CB\u2192A,\u03b1\u2032:A\u00d7CB\u2192B{displaystyle beta ‘colon Atimes _{C}Bto A,qquad alpha ‘colon Atimes _{C}Bto B}\u306e\u7d44\u3067\u3042\u308b\uff1a\u3059\u3079\u3066\u306e (a,b)\u2208A\u00d7CB{displaystyle (a,b)in Atimes _{C}B} \u306b\u5bfe\u3057\u3066 \u03b2\u2032(a,b)=a{displaystyle beta ‘(a,b)=a} \u304a\u3088\u3073 \u03b1\u2032(a,b)=b.{displaystyle alpha ‘(a,b)=b.} \u3053\u306e\u3068\u304d\u03b1\u2218\u03b2\u2032=\u03b2\u2218\u03b1\u2032{displaystyle alpha circ beta ‘=beta circ alpha ‘}\u3067\u3042\u308b\uff0e\u96c6\u5408[\u7de8\u96c6]\u96c6\u5408\u306e\u570f\u306b\u304a\u3044\u3066\uff0cf \u3068 g \u306e\u5f15\u304d\u623b\u3057\u306f\u96c6\u5408X\u00d7ZY={(x,y)\u2208X\u00d7Y\u2223f(x)=g(y)}{displaystyle Xtimes _{Z}Y={(x,y)in Xtimes Ymid f(x)=g(y)}}\u3068\u5c04\u5f71 \u03c01, \u03c02 \u306e X\u00a0\u00d7Z\u00a0Y \u3078\u306e\u5236\u9650\u306e\u7d44\u3067\u3042\u308b\uff0e\u3042\u308b\u3044\u306f\uff0cSet \u306b\u304a\u3051\u308b\u5f15\u304d\u623b\u3057\u3092\u975e\u5bfe\u79f0\u7684\u306bX\u00d7ZY\u2245\u2210x\u2208Xg\u22121[{f(x)}]\u2245\u2210y\u2208Yf\u22121[{g(y)}]{displaystyle Xtimes _{Z}Ycong coprod _{xin X}g^{-1}[{f(x)}]cong coprod _{yin Y}f^{-1}[{g(y)}]}\u3068\u898b\u308b\u3053\u3068\u3082\u3067\u304d\u308b\uff0e\u3053\u3053\u3067 \u2210{textstyle coprod } \u306f\u975e\u4ea4\u548c\u3092\u8868\u3059\uff08\u73fe\u308c\u308b\u5404\u96c6\u5408\u306f\u3001\u305d\u308c\u305e\u308c f \u307e\u305f\u306f g \u304c\u5358\u5c04\u3067\u306a\u3044\u9650\u308a\u4ea4\u308f\u308a\u3092\u6301\u3064\u3053\u3068\u306b\u6ce8\u610f\uff09\u3002\u524d\u8005\u306e\u5f0f\u306e\u5834\u5408\u3001\u5c04\u5f71 \u03c01 \u306f x \u3092\u6dfb\u5b57\u3068\u3057\u3066\u53d6\u308a\u51fa\u3059\u3053\u3068\u3001\u305d\u308c\u3068\u540c\u6642\u306b \u03c02 \u306f\u6dfb\u5b57\u3067\u3042\u308b\u3053\u3068\u3092\u5fd8\u308c\u3066\u5358\u306b Y \u306e\u5143\u3068\u307f\u308b\u3082\u306e\u306b\u306a\u3063\u3066\u3044\u308b\u3002\u3053\u306e\u4f8b\u306f\u5f15\u304d\u623b\u3057\u3092\u7279\u5fb4\u3065\u3051\u308b\u5225\u306e\u65b9\u6cd5\u3092\u52d5\u6a5f\u4ed8\u3051\u308b\uff0c\u3059\u306a\u308f\u3061\u5c04 f \u2218 p1, g \u2218 p2: X \u00d7 Y \u2192 Z \u306e\u30a4\u30b3\u30e9\u30a4\u30b6\u3067\u3042\u308b\uff0c\u305f\u3060\u3057 X\u00a0\u00d7\u00a0Y \u306f X \u3068 Y \u306e\u4e8c\u9805\u7a4d\u3067\uff0cp1 \u3068 p2 \u306f\u81ea\u7136\u306a\u5c04\u5f71\u3067\u3042\u308b\uff0e\u3053\u308c\u306f\u4e8c\u9805\u7a4d\u3068\u30a4\u30b3\u30e9\u30a4\u30b6\u3092\u6301\u3064\u4efb\u610f\u306e\u570f\u306b\u304a\u3044\u3066\u5f15\u304d\u623b\u3057\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u3059\uff0e\u5b9f\u306f\uff0c\u6975\u9650\u306e\u5b58\u5728\u5b9a\u7406\uff08\u82f1\u8a9e\u7248\uff09\u306b\u3088\u3063\u3066\uff0c\u7d42\u5bfe\u8c61\uff0c\u4e8c\u9805\u7a4d\uff0c\u30a4\u30b3\u30e9\u30a4\u30b6\u3092\u6301\u3064\u570f\u306b\u304a\u3044\u3066\uff0c\u3059\u3079\u3066\u306e\u6709\u9650\u6975\u9650\u304c\u5b58\u5728\u3059\u308b\uff0e\u30d5\u30a1\u30a4\u30d0\u30fc\u675f[\u7de8\u96c6]\u5f15\u304d\u623b\u3057\u306e\u5225\u306e\u4f8b\u306f\u30d5\u30a1\u30a4\u30d0\u30fc\u675f\u306e\u7406\u8ad6\u304b\u3089\u6765\u308b\uff0e\u675f\u5199\u50cf \u03c0: E \u2192 B \u3068\u9023\u7d9a\u5199\u50cf f:\u00a0X\u00a0\u2192\u00a0B \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\uff0c\u4f4d\u76f8\u7a7a\u9593\u306e\u570f\u306b\u304a\u3051\u308b\u5f15\u304d\u623b\u3057 X\u00a0\u00d7B\u00a0E \u306f\u5f15\u304d\u623b\u3057\u675f\uff08\u82f1\u8a9e\u7248\uff09\u3068\u547c\u3070\u308c\u308b X \u4e0a\u306e\u30d5\u30a1\u30a4\u30d0\u30fc\u675f\u3067\u3042\u308b\uff0e\u4ed8\u968f\u3059\u308b\u53ef\u63db\u56f3\u5f0f\u306f\u30d5\u30a1\u30a4\u30d0\u30fc\u675f\u306e\u5c04\u3067\u3042\u308b\uff0e\u9006\u50cf\u3068\u5171\u901a\u90e8\u5206[\u7de8\u96c6]\u5199\u50cf\u306b\u3088\u308b\u96c6\u5408\u306e\u9006\u50cf\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5f15\u304d\u623b\u3057\u3068\u3057\u3066\u8a18\u8ff0\u3067\u304d\u308b\uff0ef: A \u2192 B, B0 \u2286 B \u3068\u3059\u308b\uff0eg \u3092\u5305\u542b\u5199\u50cf B0 \u21aa B \u3068\u3059\u308b\uff0e\u3053\u306e\u3068\u304d\uff0c\uff08Set \u306b\u304a\u3051\u308b\uff09f \u3068 g \u306e\u5f15\u304d\u623b\u3057\u306f\uff0c\u539f\u50cf f\u22121[B0] \u3068\u539f\u50cf\u306e A \u3078\u306e\u5305\u542bf\u22121[B0] \u21aa A\u3068 f \u306e f\u22121[B0] \u3078\u306e\u5236\u9650f\u22121[B0] \u2192 B0\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u308b\uff0e\u3053\u306e\u4f8b\u306e\u305f\u3081\uff0c\u4e00\u822c\u306e\u570f\u306b\u304a\u3044\u3066\u5c04 f \u3068\u5358\u5c04 g \u306e\u5f15\u304d\u623b\u3057\u306f\uff0cg \u306b\u3088\u3063\u3066\u7279\u5b9a\u3055\u308c\u308b\u90e8\u5206\u5bfe\u8c61\u306e f \u306b\u3088\u308b\u300c\u539f\u50cf\u300d\u3068\u601d\u3046\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u540c\u69d8\u306b\uff0c2\u3064\u306e\u5358\u5c04\u306e\u5f15\u304d\u623b\u3057\u306f2\u3064\u306e\u90e8\u5206\u5bfe\u8c61\u306e\u300c\u5171\u901a\u90e8\u5206\u300d\u3068\u601d\u3046\u3053\u3068\u304c\u3067\u304d\u308b\uff0e\u7d42\u5bfe\u8c61 T \u3092\u6301\u3064\u4efb\u610f\u306e\u570f\u306b\u304a\u3044\u3066\uff0c\u5f15\u304d\u623b\u3057 X\u00a0\u00d7T\u00a0Y \u306f\u5358\u306b\u901a\u5e38\u306e\u7a4d X\u00a0\u00d7\u00a0Y \u3067\u3042\u308b\uff0e\u5358\u5c04\u306f\u5f15\u304d\u623b\u3057\u3067\u5b89\u5b9a\u3067\u3042\u308b\uff0c\u3059\u306a\u308f\u3061\uff0c\u4e0a\u306e\u5c04 f \u304c\u5358\u5c04\u3067\u3042\u308c\u3070\uff0c\u5c04 p2 \u3082\u5358\u5c04\u3067\u3042\u308a\uff0c\u540c\u69d8\u306b\uff0cg \u304c\u5358\u5c04\u306a\u3089\u3070 p1 \u3082\u5358\u5c04\u3067\u3042\u308b\uff0e\u540c\u578b\u5c04\u3082\u5b89\u5b9a\u3067\u3042\u308a\uff0c\u3057\u305f\u304c\u3063\u3066\uff0c\u4f8b\u3048\u3070\uff0c\u4efb\u610f\u306e\u5c04 Y\u00a0\u2192\u00a0X\uff08\u5c04 X\u00a0\u2192\u00a0X \u306f\u6052\u7b49\u5c04\uff09\u306b\u5bfe\u3057\u3066 X\u00a0\u00d7X\u00a0Y \u2245 Y \u3067\u3042\u308b\uff0e\u30a2\u30fc\u30d9\u30eb\u570f\u306f\u3059\u3079\u3066\u306e\u5f15\u304d\u623b\u3057\u304c\u5b58\u5728\u3057\uff0c\u6b21\u306e\u610f\u5473\u3067\u6838\u3092\u4fdd\u3064\uff1a \u3092\u5f15\u304d\u623b\u3057\u56f3\u5f0f\u3068\u3059\u308b\u3068\uff0c\u8a98\u5c0e\u3055\u308c\u308b\u5c04 ker(p2)\u00a0\u2192\u00a0ker(f) \u3068 ker(p1)\u00a0\u2192\u00a0ker(g) \u306f\u540c\u578b\u3067\u3042\u308b\uff0e\u3057\u305f\u304c\u3063\u3066\u3059\u3079\u3066\u306e\u5f15\u304d\u623b\u3057\u56f3\u5f0f\u306f\u6b21\u306e\u5f62\u306e\u53ef\u63db\u56f3\u5f0f\u3092\u751f\u3058\u308b\uff0c\u305f\u3060\u3057\u3059\u3079\u3066\u306e\u884c\u3068\u5217\u306f\u5b8c\u5168\u3067\u3042\u308b\uff1a00\u2193\u2193L=L\u2193\u21930\u2192K\u2192P\u2192Y\u2225\u2193\u21930\u2192K\u2192X\u2192Z.{displaystyle {begin{array}{ccccccc}&&&&0&&0\\&&&&downarrow &&downarrow \\&&&&L&=&L\\&&&&downarrow &&downarrow \\0&to &K&to &P&to &Y\\&&parallel &&downarrow &&downarrow \\0&to &K&to &X&to &Z.end{array}}}\u81ea\u7136\u306a\u540c\u578b (A\u00d7CB)\u00d7BD \u2245 A\u00d7CD \u304c\u5b58\u5728\u3059\u308b\uff0e\u660e\u793a\u7684\u306b\u306f\uff0c\u3053\u308c\u304c\u610f\u5473\u3059\u308b\u306e\u306f\uff1a\u5c04 f: A \u2192 C, g: B \u2192 C, h: D \u2192 B \u304c\u4e0e\u3048\u3089\u308c\uff0cf \u3068 g \u306e\u5f15\u304d\u623b\u3057\u304c r: P \u2192 A \u3068 s: P \u2192 B \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\uff0cs \u3068 h \u306e\u5f15\u304d\u623b\u3057\u304c t: Q \u2192 P \u3068 u: Q \u2192 D \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u308b\u306a\u3089\u3070\uff0cf \u3068 gh \u306e\u5f15\u304d\u623b\u3057\u306f rt: Q \u2192 A \u3068 u: Q \u2192 D \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u308b\uff0e\u56f3\u5f0f\u7684\u306b\u306f\uff0c\u3053\u308c\u304c\u610f\u5473\u3059\u308b\u306e\u306f\uff0c2\u3064\u306e\u5f15\u304d\u623b\u3057\u6b63\u65b9\u5f62\u3092\uff0c1\u3064\u306e\u5c04\u3092\u5171\u6709\u3059\u308b\u3088\u3046\u306b\u96a3\u306b\u4e26\u3079\u308b\u3068\uff0c\u771f\u3093\u4e2d\u306e\u5171\u6709\u3055\u308c\u305f\u5c04\u3092\u7121\u8996\u3057\u3066\uff0c\u5927\u304d\u3044\u5f15\u304d\u623b\u3057\u6b63\u65b9\u5f62\u304c\u5f97\u3089\u308c\u308b\uff0eQ\u2192tP\u2192rA\u2193u\u2193s\u2193fD\u2192hB\u2192gC{displaystyle {begin{array}{ccccc}Q&{xrightarrow {t}}&P&{xrightarrow {r}}&A\\downarrow _{u}&&downarrow _{s}&&downarrow _{f}\\D&{xrightarrow {h}}&B&{xrightarrow {g}}&Cend{array}}}\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u51fa\u5178\u306f\u5217\u6319\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u811a\u6ce8\u306a\u3069\u3092\u7528\u3044\u3066\u3069\u306e\u8a18\u8ff0\u306e\u60c5\u5831\u6e90\u3067\u3042\u308b\u304b\u3092\u660e\u8a18\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u3092\u304a\u9858\u3044\u3044\u305f\u3057\u307e\u3059\u3002\uff082017\u5e749\u6708\uff09Ad\u00e1mek, Ji\u0159\u00ed, Herrlich, Horst, & Strecker, George E.; (1990). Abstract and Concrete Categories (4.2MB PDF). Originally publ. John Wiley & Sons. ISBN\u00a00-471-60922-6. (now free on-line edition).Cohn, Paul M.; Universal Algebra (1981), D.Reidel Publishing, Holland, ISBN\u00a090-277-1213-1 (Originally published in 1965, by Harper & Row).Takeshi, SAITO.; \u00c9l\u00e9ments de Math\u00e9matique (2020), University of Tokyo Press, ISBN\u00a0978-4-13-063904-0.\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki25\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki25\/archives\/291803#breadcrumbitem","name":"\u5f15\u304d\u623b\u3057 (\u570f\u8ad6) – Wikipedia"}}]}]