Braided monoidal category

In mathematics, a commutativity constraint γ {\displaystyle \gamma } on a monoidal category C {\displaystyle {\mathcal {C}}} is a choice of isomorphism γ A , B : A ⊗ B → B ⊗ A {\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 A ⊗ B ≅ B ⊗ A {\displaystyle A\otimes B\cong B\otimes A} for all pairs of objects A , B ∈ C {\displaystyle A,B\in {\mathcal {C}}} .

Source: Wikipedia — Braided monoidal category (CC BY-SA 4.0)