Memoirs of the American Mathematical Society 1995; 81 pp; softcover Volume: 117 ISBN10: 0821803441 ISBN13: 9780821803448 List Price: US$39 Individual Members: US$23.40 Institutional Members: US$31.20 Order Code: MEMO/117/558
 The need to address the appropriate threedimensional generalization of category (tricategory) has been felt in homotopy theory, lowdimensional topology, cohomology theory, category theory, and quantum field theory. Benabou's bicategories provide the twodimensional 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 2categories 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 2categories
Readership Research mathematicians, theoretical physicists, algebraic topologists, 3D 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
