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 Internal monoids 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.

Last revised on May 27, 2011 at 11:20:35.
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