category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
monoidal dagger-category?
An (∞,n)-category with adjoints (see there for more) and a (fully) dual object for every object.
Let $C$ be an (∞,n)-category. We say that
$C$ has adjoints for morphisms if in its homotopy 2-category every morphism has a left adjoint and a right adjoint;
for $1 \lt k \lt n$ that $C$ has adjoints for k-morphisms if for every pair $X,Y \in C$ of objects, the hom-(∞,n-1)-category $C(X,Y)$ has adjoints for $(k-1)$-morphisms.
$C$ is an (∞,n)-category with adjoints if it has adjoints for k-morphisms with $0 \lt k \lt n$.
If $C$ 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 $(\infty,n)$-categories with duals seems plausible to be aximatized inside opetopic type theory.
fundamental n-category?
For more see at (infinity,n)-category with adjoints.
Last revised on November 6, 2014 at 18:29:25. See the history of this page for a list of all contributions to it.