Coherence for tricategories
About this Title
R. Gordon, A. J. Power and Ross Street
Publication: Memoirs of the American Mathematical Society
Publication Year
1995: Volume 117, Number 558
ISBNs: 978-0-8218-0344-8 (print); 978-1-4704-0137-5 (online)
DOI: http://dx.doi.org/10.1090/memo/0558
MathSciNet review: 1261589
MSC: Primary 18D05
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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
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
