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Coherence in three-dimensional category theory / Nick Gurski, University of Sheffield.
| Author/creator | Gurski, Nick, 1980- |
| Format | Electronic |
| Publication Info | Cambridge : Cambridge University Press, 2013. |
| Description | vii, 278 pages : illustrations ; 24 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Cambridge tracts in mathematics ; 201 |
| Contents | Machine generated contents note: 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. |
| Abstract | "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"-- Provided by publisher. |
| Abstract | "In the study of higher categories, dimension three occupies an interesting position on the landscape of higher dimensional category theory. From the perspective of a "hands-on" approach to defining weak n-categories, tricategories represent the most complicated kind of higher category that the community at large seems comfortable working with. "-- Provided by publisher. |
| Bibliography note | Includes bibliographical references (pages 273-276) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2012051079 |
| ISBN | 9781107034891 (hardback) |