# nLab pivotal category

### Context

#### Monoidal categories

monoidal categories

# 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)