category with duals (list of them)
dualizable object (what they have)
abstract duality: opposite category,
A dualizable object in a symmetric monoidal (∞,n)-category is called fully dualizable if the structure maps of the duality unit and counit each themselves have adjoints, which have adjoints, and so on, up to level .
In the 2-category of associative algebras with bimodules between them as morphisms, over a perfect field, fully dualizable objects separable algebras which are a projective module over SchommerPries 11, section 3.8.3.
|geometry||monoidal category theory||category theory|
|perfect module||(fully-)dualizable object||compact object|
The definition appears around claim 2.3.19 of
Detailed discussion in degree 2 and 3 appears in