| eBook 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 |
| eBook 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 |
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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.
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Table of Contents
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Chapters
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1. Introduction
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2. The definition of tricategory
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3. Trihomomorphisms, triequivalence, and $\mathbf {Tricat}(T, S)$
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4. Cubical functors and tricategories, and the monoidal category Gray
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5. Gray-categories, and Bicat as a tricategory
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6. The Gray-category $\mathbf {Prep}(T)$ of prerepresentations of $T$
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7. The “Yoneda embedding”
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8. The main theorem
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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
