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

• Introduction
• The definition of tricategory
• Trihomomorphisms, triequivalence, and \(\operatorname{\mathbf{Tricat}}(T,S)\)
• Cubical functors and tricategories, and the monoidal category \(\operatorname{\mathbf{Gray}}\)
• \(\operatorname{\mathbf{Gray}}\)-categories, and \(\operatorname{\mathbf{Bicat}}\) as a tricategory
• The \(\operatorname{\mathbf{Gray}}\)-category \(\operatorname{Prep(T)}\) of prerepresentations of \(T\)
• The "Yoneda Embedding"
• The Main Theorem
• Acknowledgements
• References