Braided monoidal category
MONOIDAL CATEGORY WHERE A ⊗ B IS EQUIVALENT TO B ⊗ A, GENERALIZED SO THE MAPS MAY NOT BE INVERSES
Braided tensor category; Braided monoidal categories
In mathematics, a commutativity constraint \gamma on a monoidal category \mathcal{C} is a choice of isomorphism \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 A \otimes B \cong B \otimes A for all pairs of objects A,B \in \mathcal{C}.