Coherence in three-dimensional category theory
QA169 .G87 2013
- Unknown QA169 .G87 2013
- Includes bibliographical references (pages 273-276) and index.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
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- Publication date
- Nick Gurski, University of Sheffield.
- Cambridge tracts in mathematics ; 201