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Coherence for Tricategories
 
R. Gordon Temple University
A. J. Power University of Edinburgh
Ross Street Macquarie University
Coherence for Tricategories
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
Coherence for Tricategories
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Coherence for Tricategories
R. Gordon Temple University
A. J. Power University of Edinburgh
Ross Street Macquarie University
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
  • 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
    Readership

    Research 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    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
Readership

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 publishers of book reviews
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.