## Finite tensor categories

Venue: | Moscow Math. Journal |

Citations: | 26 - 8 self |

### BibTeX

@ARTICLE{Etingof_finitetensor,

author = {P. Etingof and S. Gelaki and D. Nikshych and V. Ostrik},

title = {Finite tensor categories},

journal = {Moscow Math. Journal},

year = {},

pages = {627--654}

}

### OpenURL

### Abstract

These are lecture notes for the course 18.769 “Tensor categories”, taught by P. Etingof at MIT in the spring of 2009. In these notes we will assume that the reader is familiar with the basic theory of categories and functors; a detailed discussion of this theory can be found in the book [ML]. We will also assume the basics of the theory of abelian categories (for a more detailed treatment see the book [F]). If C is a category, the notation X ∈ C will mean that X is an object of C, and the set of morphisms between X, Y ∈ C will be denoted by Hom(X, Y). Throughout the notes, for simplicity we will assume that the ground field k is algebraically closed unless otherwise specified, even though in many cases this assumption will not be needed. 1. Monoidal categories 1.1. The definition of a monoidal category. A good way of thinking