nLab
pivotal category

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.