# nLab spherical category

Spherical categories

### Context

#### Monoidal categories

monoidal categories

# 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 2-sphere.

## Definition

A spherical category is a pivotal category $\mathcal{C}$ where the left and right trace operations coincide on all objects.

If $\mathcal{C}$ is in addition a tensor category so that this trace may be interpreted as an element of the ground field, then the trace $tr\big( id_X\big)$ is called the quantum dimension of the object $X$ (e.g. FRS02 (2.17))

## References

The definition is originally due to:

Review:

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Last revised on May 26, 2022 at 06:38:14. See the history of this page for a list of all contributions to it.