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Coherence for Tricategories

R. Gordon Temple University
A. J. Power University of Edinburgh
Ross Street Macquarie University
Available Formats:
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 Click above image for expanded view Coherence for Tricategories R. Gordon Temple University A. J. Power University of Edinburgh Ross Street Macquarie University Available Formats:  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 Details

Memoirs of the American Mathematical Society
Volume: 1171995; 81 pp
MSC: 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

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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1171995; 81 pp
MSC: 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

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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.