#
nLab

spherical 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

## 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)

Revised on May 27, 2011 11:02:44
by

Urs Schreiber
(195.37.234.90)