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
homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
The coherence theorem for 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 monoidal bicategory commutes; in other words, any two parallel composites of constraint 2-cells are equal. Moreover, any two parallel composites of constraint 1-cells are uniquely isomorphic.
Every monoidal bicategory is equivalent to a Gray-monoid.
The second version is a direct corollary of the coherence theorem for tricategories. The first can then be deduced from it (not entirely trivially).
Gordon, Power, Street, Coherence for tricategories, Mem. Amer. Math Soc. 117 (1995) no 558
Nick Gurski, Coherence in three-dimensional category theory
Last revised on October 7, 2012 at 20:41:45. See the history of this page for a list of all contributions to it.