Coherence in Three-Dimensional Category Theory - Free eBook Download
Book Details
Hardcover: 286 pages
Publisher: Cambridge University Press (May 6, 2013)
Language: English
ISBN-10: 1107034892
ISBN-13: 978-1107034891
File Size: 3.5 Mb | File Format: PDF
Book Description
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.
Book Description
About the Author
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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