Braided monoidal category

In mathematics, a commutativity constraint ${\displaystyle \gamma }$ on a monoidal category ${\displaystyle {\mathcal {C}}}$ is a choice of isomorphism ${\displaystyle \gamma _{A,B}:A\otimes B\rightarrow B\otimes A}$ for each pair of objects A and B which form a "natural family." In particular, to have a commutativity constraint, one must have ${\displaystyle A\otimes B\cong B\otimes A}$ for all pairs of objects ${\displaystyle A,B\in {\mathcal {C}}}$.

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