Coherence in Three-Dimensional Category Theory

1. Auflage 2013
ISBN: 978-1-107-03489-1
Verlag: Cambridge University Press

Buch, Englisch, Band 201, 286 Seiten, Format (B × H): 156 mm x 236 mm, Gewicht: 519 g

Reihe: 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.

Autoren/Hrsg.

Gurski, Nick

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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.

Über Autor(innen)

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