nLab
tensor category

Context

Monoidal categories

With symmetry

With duals for objects

  • (list of them)

  • (what they have)

  • , a.k.a.

  • , a.k.a.

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

  • (, , , )

Internal monoids

Examples

Theorems

In higher category theory

Category theory

Concepts

Universal constructions

    • /

    • /

Theorems

Extensions

Applications

Contents

Idea

A tensor category is a category equipped with an operation similar to the tensor product in Ab.

The precise definition associated with the term “tensor category” varies somewhat in the literature.

It may mean any :

Properties

Tannaka theory, Deligne’s theorem, super-representation theory

Deligne's theorem on tensor categories (Deligne 02) establishes Tannaka duality between sufficiently well-behaved linear tensor categories in characteristic zero and supergroups, realizing these tensor categories as categories of representations of these supergroups.

References

Deligne's theorem on tensor categories is due to

  • Pierre Deligne, Catégorie Tensorielle, Moscow Math. Journal 2 (2002) no. 2, 227-248. (pdf)

Review includes

Last revised on November 25, 2016 at 03:42:45. See the history of this page for a list of all contributions to it.