nLab
tensor category

Contents

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

Category theory

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 February 3, 2019 at 05:49:59. See the history of this page for a list of all contributions to it.