**Memoirs of the American Mathematical Society**

1995;
81 pp;
Softcover

MSC: Primary 18;

Print ISBN: 978-0-8218-0344-8

Product Code: MEMO/117/558

List Price: $39.00

Individual Member Price: $23.40

**Electronic ISBN: 978-1-4704-0137-5
Product Code: MEMO/117/558.E**

List Price: $39.00

Individual Member Price: $23.40

# Coherence for Tricategories

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*R. Gordon; A. J. Power; Ross Street*

The need to address the appropriate
three-dimensional generalization of category (tricategory) has been felt
in homotopy theory, low-dimensional topology, cohomology theory,
category theory, and quantum field theory. Benabou's bicategories
provide the two-dimensional notion into which examples naturally fit.
In developing the theory of bicategories it is very reassuring to
know the coherence theorem: They can be replaced by the
stricter 2-categories which are merely categories enriched in the
category of categories.

In this book, the authors provide…

- the unique source of the full definition of tricategory
- a thorough and complete proof of the coherence theorem for tricategories
- a wholly modern source of material on Gray's tensor product of 2-categories

#### Table of Contents

# Table of Contents

## Coherence for Tricategories

- Contents v6 free
- Abstract vi7 free
- 1. Introduction 18 free
- 2. The Definition of Tricategory 714 free
- 3. Trihomomorphisms, Triequivalence, and Tricat(T, 5) 1522
- 4. Cubical Functors and Tricategories, and the Monoidal Category Gray 3138
- 5. Gray-categories, and Bicat as a Tricategory 4148
- 6. The Gray-category Prep(T) of Prerepresentations of T 5562
- 7. The "Yoneda Embedding" 6471
- 8. The Main Theorem 7481
- Acknowledgements 7885
- References 7986

#### Readership

Research mathematicians, theoretical physicists, algebraic topologists, 3-D computer scientists, and theoretical computer scientists.