**Mathematical Surveys and Monographs**

Volume: 205;
2015;
344 pp;
Softcover

MSC: Primary 17; 18; 19; 20;

**Print ISBN: 978-1-4704-3441-0
Product Code: SURV/205.S**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-1-4704-2349-0
Product Code: SURV/205.E**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

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#### Supplemental Materials

# Tensor Categories

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*Pavel Etingof; Shlomo Gelaki; Dmitri Nikshych; Victor Ostrik*

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

# Table of Contents

## Tensor Categories

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface xi12
- Chapter 1. Abelian categories 118
- Chapter 2. Monoidal categories 2138
- Chapter 3. ℤ₊-rings 4966
- Chapter 4. Tensor categories 6582
- Chapter 5. Representation categories of Hopf algebras 91108
- Chapter 6. Finite tensor categories 119136
- Chapter 7. Module categories 131148
- Chapter 8. Braided categories 195212
- Chapter 9. Fusion categories 275292
- Bibliography 325342
- Index 339356
- Back Cover Back Cover1362