| Electronic ISBN: | 978-1-4704-0137-5 |
| 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 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
ReadershipResearch mathematicians, theoretical physicists, algebraic topologists, 3-D 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. Gray-categories, and Bicat as a tricategory
-
6. The Gray-category $\mathbf {Prep}(T)$ of prerepresentations of $T$
-
7. The “Yoneda embedding”
-
8. The main theorem
-
-
RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
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
Research mathematicians, theoretical physicists, algebraic topologists, 3-D 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. Gray-categories, and Bicat as a tricategory
-
6. The Gray-category $\mathbf {Prep}(T)$ of prerepresentations of $T$
-
7. The “Yoneda embedding”
-
8. The main theorem
