Coherence in Three-Dimensional Category Theory Front Cover

Coherence in Three-Dimensional Category Theory


Coherence in Three-Dimensional Category Theory (Cambridge Tracts in Mathematics)
Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science.

Table of Contents

Part I. Background:
1. Bicategorical background
2. Coherence for bicategories
3. Gray-categories
Part II. Tricategories:
4. The algebraic definition of tricategory
5. Examples
6. Free constructions
7. Basic structure
8. Gray-categories and tricategories
9. Coherence via Yoneda
10. Coherence via free constructions
Part III. Gray monads:
11. Codescent in Gray-categories
12. Codescent as a weighted colimit
13. Gray-monads and their algebras
14. The reflection of lax algebras into strict algebras
15. A general coherence result

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