nLab
spherical category

Spherical categories

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

Spherical categories

Idea

A spherical category is a monoidal category with duals that behaves as if its morphisms can be drawn and moved around on a sphere.

Definition

A spherical category is a pivotal category where the left and right trace operations coincide on all objects.

References

The definition is originally due to

A review is in section 2.3 of

  • Michael Müger, From Subfactors to Categories and Topology I. Frobenius algebras in and Morita equivalence of tensor categories (arXiv:0111204)

More is in

Last revised on November 17, 2014 at 23:09:30. See the history of this page for a list of all contributions to it.