With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
The coherence theorem for braided monoidal bicategories, like many coherence theorems, has several forms (or, alternatively, refers to several different theorems):
Every diagram of constraint 2-cells in a free braided monoidal bicategory commutes; in other words, any two parallel composites of constraint 2-cells are equal. Moreover, two parallel composites of constraint 1-cells are isomorphic if and only if they have the same underlying braid, in which case they are uniquely isomorphic.
Every braided monoidal bicategory is equivalent to a strict braided monoidal bicategory.
Last revised on October 7, 2012 at 20:42:34. See the history of this page for a list of all contributions to it.