nLab
pivotal category

Contents

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

Internal monoids

Examples

Theorems

In higher category theory

Contents

Definition

A pivotal category is an autonomous category equipped with a monoidal natural isomorphism A(A *) *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.

Last revised on May 27, 2011 at 11:20:35. See the history of this page for a list of all contributions to it.