| has gloss | eng: In mathematics, a commutativity constraint on a monoidal category \mathcalC} is a natural isomorphism \gamma from \mathcalC} to \mathcalC}^op}, where \mathcalC}^op} is the category with the opposite tensor product. Explicitly, \gamma is a choice of isomorphism \gamma_A,B}:A\otimes B \rightarrow B\otimes A for each pair of objects A and B which are form a "natural family". In particular to have a commutativity constraint, one must have A \otimes B \cong B \otimes A for all pairs of objects A,B \in \mathcalC}. |
