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).
For example, in Vect, the braiding maps (a typical generator of ) to . But a braiding is most interesting when it does not look like something trivial like that.
Revised on April 26, 2010 00:04:25
by Toby Bartels