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 symmetric 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 symmetric 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 permutation, in which case they are uniquely isomorphic.
Every symmetric monoidal bicategory is equivalent to a strict symmetric monoidal bicategory.
Nick Gurski and Angelica Osorno, “Infinite loop spaces, and
coherence for symmetric monoidal bicategories“, arXiv
Bruce Bartlett, “Quasistrict symmetric monoidal 2-categories via wire diagrams”, arXiv
Bruce Bartlett, “Quasistrict symmetric monoidal 2-categories via wire diagrams”, n-Cafe
Despite the terminology, the result by Chris Schommer-Pries explained by Bruce Bartlett goes further than the earlier result of Gurski and Osorno. The result in the n-Cafe post seems to go even further.
Last revised on February 21, 2015 at 23:49:19. See the history of this page for a list of all contributions to it.