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Coherence in three-dimensional category theory / Nick Gurski, University of Sheffield.

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Author/Creator:
Gurski, Nick, 1980-
Language:
English.
Publication date:
2013
Publication:
Cambridge : Cambridge University Press, 2013.
Format:
  • Book
  • vii, 278 pages : illustrations ; 24 cm.
Bibliography:
Includes bibliographical references (pages 273-276) and index.
Contents:
  • Bicategorical background
  • Coherence for bicategories
  • Gray-categories
  • Tricategories: The algebraic definition of tricategory
  • Examples
  • Free constructions
  • Basic structure
  • Gray-categories and tricategories
  • Coherence via Yoneda
  • Coherence via free constructions
  • Gray monads. Codescent in Gray-categories
  • Codescent as a weighted colimit
  • Gray-monads and their algebras
  • The reflection of lax algebras into strict algebras
  • A general coherence result.
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"--Provided by publisher.
Series:
Cambridge tracts in mathematics ; 201.
Subjects:
ISBN:
9781107034891
1107034892

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