Braided monoidal category

Summary

A braided monoidal category is a monoidal category with a natural isomorphism $A \otimes B \to B \otimes A$, the braiding, compatible with the associator. The braiding need not square to the identity, and its behaviour is modelled by the braid groups rather than the symmetric groups. Braided monoidal categories arise from representations of quantum groups and give invariants of knots and links. When the braiding squares to the identity the category is symmetric.