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center:The Center of European Languages of Qom(Ale Beit Publications)
Document Type:BL
Record Number:1651
Doc. No:b11733
Language of Document :English
Main Entry:Gurski, Nick, 1980
Title & Author:Coherence in three-dimensional category theory/ Nick Gurski, University of Sheffield
Series Statement :(Cambridge tracts in mathematics ; 201)
Page. NO:vii, 278 pages: illustrations ; 24 cm.
ISBN:9781107034891(hardback)
Notes:Print
Bibliographies/Indexes:Includes bibliographical references (pages 273-276) and index.
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.
"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.
"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.
Subject:Tricategories
Subject:MATHEMATICS / Logic.bisacsh
Dewey Classification:‭512.55‬
LC Classification:‭QA169‬‭.G87 2013‬