With duals for objects
With duals for morphisms
Special sorts of products
In higher category theory
Any braided monoidal category has a natural isomorphism
called the braiding.
A braided monoidal category is symmetric if and only if and are inverses (although they are isomorphisms regardless).
In Vect or Mod, the braiding maps elements of a tensor product of modules to .
For the tensor product of chain complexes or that of super vector spaces there is in addition a sign .
Revised on March 1, 2016 06:48:56
by Urs Schreiber