# Coherence in Three-Dimensional Category Theory

- Length: 286 pages
- Edition: 1
- Language: English
- Publisher: Cambridge University Press
- Publication Date: 2013-05-06
- ISBN-10: 1107034892
- ISBN-13: 9781107034891
- Sales Rank: #5685574 (See Top 100 Books)

Coherence in Three-Dimensional Category Theory (Cambridge Tracts in Mathematics)

Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science.

### Table of Contents

Introduction

Part I. Background:

1. Bicategorical background

2. Coherence for bicategories

3. Gray-categories

Part II. Tricategories:

4. The algebraic definition of tricategory

5. Examples

6. Free constructions

7. Basic structure

8. Gray-categories and tricategories

9. Coherence via Yoneda

10. Coherence via free constructions

Part III. Gray monads:

11. Codescent in Gray-categories

12. Codescent as a weighted colimit

13. Gray-monads and their algebras

14. The reflection of lax algebras into strict algebras

15. A general coherence result

Bibliography

Index.