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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 Symmetric monoidal category ： ウィキペディア英語版 Symmetric monoidal category In category theory, a branch of mathematics, a symmetric monoidal category is a braided monoidal category that is maximally symmetric. That is, the braiding operator $s\_$ obeys an additional identity: $s\_\backslash circ\; s\_=1\_$. The classifying space (geometric realization of the nerve) of a symmetric monoidal category is an $E\_\backslash infty$ space, so its group completion is an infinite loop space.〔R.W. Thomason, ("Symmetric Monoidal Categories Model all Connective Spectra" ), ''Theory and Applications of Categories'', Vol. 1, No. 5, 1995, pp. 78– 118.〕 ==Definition== A symmetric monoidal category is a monoidal category (''C'', ⊗) such that, for every pair ''A'', ''B'' of objects in ''C'', there is an isomorphism $s\_:\; A\; \backslash otimes\; B\; \backslash simeq\; B\; \backslash otimes\; A$ that is natural in both ''A'' and ''B'' and such that the following diagrams commute: *The unit coherence: *:File:symmetric monoidal unit coherence.png *The associativity coherence: *:File:symmetric monoidal associativity coherence.png *The inverse law: *:File:symmetric monoidal inverse law.png In the diagrams above, ''a'', ''l'' , ''r'' are the associativity isomorphism, the left unit isomorphism, and the right unit isomorphism respectively. 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「Symmetric monoidal category」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.