Coherence in Three-Dimensional Category Theory

Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.

Nick Gurski (Author)

9781107034891, Cambridge University Press

Hardback, published 21 March 2013

286 pages
23.6 x 15.5 x 1.9 cm, 0.51 kg

'Despite the complexity of the issue, the detailed treatment of the subject, fairly typical of the author, leaves no room for ambiguity, and the text can be followed very well by any attentive reader.' Josep Elgueta, Mathematical Reviews

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.

Introduction
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
Bibliography
Index.

Subject Areas: Algebraic topology [PBPD], Algebra [PBF], Mathematics [PB]