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 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.