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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 Braided monoidal category ： ウィキペディア英語版 Braided monoidal category In mathematics, a ''commutativity constraint'' $\backslash gamma$ on a monoidal category ''$\backslash mathcal$'' is a choice of isomorphism $\backslash gamma\_:A\backslash otimes\; B\; \backslash rightarrow\; B\backslash otimes\; A$ for each pair of objects A and B which form a "natural family." In particular, to have a commutativity constraint, one must have $A\; \backslash otimes\; B\; \backslash cong\; B\; \backslash otimes\; A$ for all pairs of objects $A,B\; \backslash in\; \backslash mathcal$. A braided monoidal category is a monoidal category $\backslash mathcal$ equipped with a braiding - that is, a commutativity constraint $\backslash gamma$ that satisfies the hexagon identities (see below). The term braided comes from the fact that the braid group plays an important role in the theory of braided monoidal categories. Partly for this reason, braided monoidal categories and various related notions are important in the theory of knot invariants. Alternatively, a braided monoidal category can be seen as a tricategory with one 0-cell and one 1-cell. ==The hexagon identities== For $\backslash mathcal$ along with the commutativity constraint $\backslash gamma$ to be called a braided monoidal category, the following hexagonal diagrams must commute for all objects $A,B,C\; \backslash in\; \backslash mathcal$. Here $\backslash alpha$ is the associativity isomorphism coming from the monoidal structure on $\backslash mathcal$: 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「Braided 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.