Coherence in Three-Dimensional Category Theory

Nick Gurski (University of Sheffield)

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English

Cambridge University Press
21 March 2013

Mathematics; Algebra; Algebraic topology

Series: 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.

By: Nick Gurski (University of Sheffield)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 201
Dimensions: Height: 236mm, Width: 155mm, Spine: 19mm
Weight: 510g
ISBN: 9781107034891
ISBN 10: 1107034892
Series: Cambridge Tracts in Mathematics
Pages: 286
Publication Date: 21 March 2013
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Nick Gurski is a Lecturer in the School of Mathematics and Statistics at the University of Sheffield.

Reviews for Coherence in Three-Dimensional Category Theory

'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