nLab
pivotal category
Context
Monoidal categories
monoidal categories

With symmetry
With duals for objects
With duals for morphisms
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Examples
Theorems
In higher category theory
Contents
Definition
A pivotal category is an autonomous category equipped with a monoidal natural isomorphism $A \to (A^*)^*$ . Pivotal categories have also been called “sovereign categories.” This is a kind of category with duals .

A right autonomous category with such an isomorphism is automatically left autonomous too, so the right/left distinction does not apply to pivotal categories.

Revised on May 27, 2011 11:20:35
by

Urs Schreiber
(195.37.234.90)