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In mathematics, a ''commutativity constraint'' on a monoidal category '''' is a choice of isomorphism for each pair of objects A and B which form a "natural family." In particular, to have a commutativity constraint, one must have for all pairs of objects . A braided monoidal category is a monoidal category equipped with a braiding - that is, a commutativity constraint 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 along with the commutativity constraint to be called a braided monoidal category, the following hexagonal diagrams must commute for all objects . Here is the associativity isomorphism coming from the monoidal structure on : 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
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