# 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 literatur.

It may mean: * any monoidal category, * specifically a symmetric monoidal category (and then a quasitensor category is a braided monoidal category), * an additive (symmetric) monoidal category, * an Ab-enriched or Vect-enriched (symmetric) monoidal category.

## 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)

Discussion with an eye towards superalgebra is in

Revised on May 24, 2014 03:30:13 by Urs Schreiber (82.113.121.57)