homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
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
An (∞,n)-category with adjoints (see there for more) and a (fully) dual object for every object.
Let be an (∞,n)-category. We say that
has adjoints for morphisms if in its homotopy 2-category every morphism has a left adjoint and a right adjoint;
for that has adjoints for k-morphisms if for every pair of objects, the hom-(∞,n-1)-category has adjoints for -morphisms.
is an (∞,n)-category with adjoints if it has adjoints for k-morphisms with .
If is in addition a symmetric monoidal (∞,n)-category we say that
Finally we say that
This is (Lurie, def. 2.3.13, def. 2.3.16). See at fully dualizable object
The internal language of -categories with duals seems plausible to be axiomatized inside opetopic type theory.
fundamental n-category?
For more see at (infinity,n)-category with adjoints.
Last revised on November 17, 2022 at 12:40:57. See the history of this page for a list of all contributions to it.