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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Coherence theorem ： ウィキペディア英語版 Coherence theorem In mathematics and particularly category theory, a coherence theorem is a tool for proving a coherence condition. Typically a coherence condition requires an infinite number of equalities among compositions of structure maps. A coherence theorem states that, in order to be assured that all these equalities hold, it suffices to check a small number of identities. ==Examples== Consider the case of a monoidal category. Recall that part of the data of a monoidal category is an ''associator'', which is a choice of morphism : $\backslash alpha\_\; \backslash colon\; (A\backslash otimes\; B)\backslash otimes\; C\; \backslash rightarrow\; A\backslash otimes(B\backslash otimes\; C)$ for each triple of objects $A,B,C$. Mac Lane's coherence theorem states that, provided the following diagram commutes for all quadruples of objects $A,B,C,\; D$, any pair of morphisms from $(\; (\; \backslash cdots\; (\; A\_N\; \backslash otimes\; A\_\; )\; \backslash otimes\; \backslash cdots\; )\; \backslash otimes\; A\_2\; )\; \backslash otimes\; A\_1)$ to $(\; A\_N\; \backslash otimes\; (\; A\_\; \backslash otimes\; (\; \backslash cdots\; \backslash otimes\; (\; A\_2\; \backslash otimes\; A\_1)\; \backslash cdots\; )\; )$ constructed as compositions of various $\backslash alpha\_$ are equal. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Coherence theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.