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 2-sphere.

Definition

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

If 𝒞\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(id X)tr\big( id_X\big) is called the quantum dimension of the object XX (e.g. FRS02 (2.17))

References

The definition is originally due to:

Review:

More is in:

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