Electronic ISBN:  9781470401375 
Product Code:  MEMO/117/558.E 
List Price:  $39.00 
MAA Member Price:  $35.10 
AMS Member Price:  $23.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 117; 1995; 81 ppMSC: Primary 18;
The need to address the appropriate threedimensional generalization of category (tricategory) has been felt in homotopy theory, lowdimensional topology, cohomology theory, category theory, and quantum field theory. Benabou's bicategories provide the twodimensional 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 2categories 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 2categories
ReadershipResearch mathematicians, theoretical physicists, algebraic topologists, 3D computer scientists, and theoretical computer scientists.

Table of Contents

Chapters

1. Introduction

2. The definition of tricategory

3. Trihomomorphisms, triequivalence, and $\mathbf {Tricat}(T, S)$

4. Cubical functors and tricategories, and the monoidal category Gray

5. Graycategories, and Bicat as a tricategory

6. The Graycategory $\mathbf {Prep}(T)$ of prerepresentations of $T$

7. The “Yoneda embedding”

8. The main theorem


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The need to address the appropriate threedimensional generalization of category (tricategory) has been felt in homotopy theory, lowdimensional topology, cohomology theory, category theory, and quantum field theory. Benabou's bicategories provide the twodimensional 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 2categories 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 2categories
Research mathematicians, theoretical physicists, algebraic topologists, 3D computer scientists, and theoretical computer scientists.

Chapters

1. Introduction

2. The definition of tricategory

3. Trihomomorphisms, triequivalence, and $\mathbf {Tricat}(T, S)$

4. Cubical functors and tricategories, and the monoidal category Gray

5. Graycategories, and Bicat as a tricategory

6. The Graycategory $\mathbf {Prep}(T)$ of prerepresentations of $T$

7. The “Yoneda embedding”

8. The main theorem