Braiding ($c_{X,Y}$)

The natural tensor interchange isomorphism in a braided monoidal category, constrained by the two hexagon axioms.

The compatibility equations between braiding and the associator in a braided monoidal category. Omitting the associators from the notation, they read $c_{a,b\otimes c}=(1_b\otimes c_{a,c})(c_{a,b}\otimes 1_c)$ and $c_{a\otimes b,c}=(c_{a,c}\otimes 1_b)(1_a\otimes c_{b,c})$. Thus exchanging a composite with another object is the sequence of exchanges of its factors.