Symmetric monoidal category

Summary

A symmetric monoidal category is a braided monoidal category whose braiding, applied twice, gives the identity. It is the categorical form of a commutative operation: $A \otimes B$ and $B \otimes A$ are identified by a swap that undoes itself. Sets with the Cartesian product, vector spaces with the tensor product, and modules over a commutative ring are symmetric monoidal. Symmetric monoidal categories are the setting of commutative monoid objects, of topological quantum field theories and of linear logic.