category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
monoidal dagger-category?
Any braided monoidal category has a natural isomorphism
called the braiding.
A braided monoidal category is symmetric if and only if $B_{x,y}$ and $B_{y,x}$ are inverses (although they are isomorphisms regardless).
In Vect or Mod, the braiding maps elements $a\otimes b$ of a tensor product of modules $X \otimes Y$ to $b \otimes a$.
For the tensor product of chain complexes or that of super vector spaces there is in addition a sign $a \otimes b \mapsto (-1)^{deg(a) deg(b)} (b \otimes a)$.
For more see at signs in supergeometry.
Last revised on July 26, 2018 at 12:24:34. See the history of this page for a list of all contributions to it.