With duals for objects
With duals for morphisms
Special sorts of products
In higher category theory
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.
- 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