# nLab tensor category

### Context

#### Monoidal categories

monoidal categories

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

• Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik, Topics in Lie theory and Tensor categories – 9 Tensor categories, Lecture notes (spring 2009) (pdf web)
• Pierre Deligne, Catégorie Tensorielle, Moscow Math. Journal 2 (2002) no. 2, 227-248. (pdf)

Review includes

Revised on March 31, 2015 10:57:03 by Urs Schreiber (195.113.30.252)