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
abstract duality: opposite category,
concrete duality: dual object, dualizable object, fully dualizable object, dualizing object
Examples
between higher geometry/higher algebra
Langlands duality, geometric Langlands duality, quantum geometric Langlands duality
In QFT and String theory
In a monoidal category, a dualizable object $A$ for which the structure unit (and counit) maps between $A \otimes A^\ast$ (and $A^\ast \otimes A$) and the unit object are isomorphisms is called an invertible object.
A monoidal category in which all objects are invertible is called a 2-group.
In terms of linear type theory one might speak of invertible types.
Last revised on May 26, 2023 at 17:16:57. See the history of this page for a list of all contributions to it.