# Tensor Categories

### About this Title

**Pavel Etingof**, *Massachusetts Institute of Technology, Cambridge, MA*, **Shlomo Gelaki**, *Technion-Israel Institute of Technology, Haifa, Israel*, **Dmitri Nikshych**, *University of New Hampshire, Durham, NH* and **Victor Ostrik**, *University of Oregon, Eugene, OR*

Publication: Mathematical Surveys and Monographs

Publication Year:
2015; Volume 205

ISBNs: 978-1-4704-2024-6 (print); 978-1-4704-2349-0 (online)

DOI: https://doi.org/http://dx.doi.org/10.1090/surv/205

MathSciNet review: MR3242743

MSC: Primary 18D10; Secondary 16T20

Read more about this volume

Is there a vector space whose dimension is the golden ratio? Of course
not—the golden ratio is not an integer! But this can happen for
generalizations of vector spaces—objects of a tensor category. The
theory of tensor categories is a relatively new field of mathematics
that generalizes the theory of group representations. It has deep
connections with many other fields, including representation theory,
Hopf algebras, operator algebras, low-dimensional topology (in
particular, knot theory), homotopy theory, quantum mechanics and field
theory, quantum computation, theory of motives, etc. This book gives a
systematic introduction to this theory and a review of its
applications. While giving a detailed overview of general tensor
categories, it focuses especially on the theory of finite tensor
categories and fusion categories (in particular, braided and modular
ones), and discusses the main results about them with proofs. In
particular, it shows how the main properties of finite-dimensional
Hopf algebras may be derived from the theory of tensor categories.

Many important results are presented as a sequence of exercises,
which makes the book valuable for students and suitable for graduate
courses. Many applications, connections to other areas, additional
results, and references are discussed at the end of each chapter.

Readership

Graduate students and research mathematicians interested in
category theory and Hopf algebras.

### Table of Contents

**Front/Back Matter**

**Chapters**

**View full volume PDF**