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Coherence in Three-Dimensional Category Theory

Part of Cambridge Tracts in Mathematics

  • Date Published: May 2013
  • availability: In stock
  • format: Hardback
  • isbn: 9781107034891

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  • 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.

    • A key reference containing background material for a wide variety of relevant topics
    • Self-contained treatment of all the main results
    • Includes important explicit examples of tricategories, which will be useful for applications in other fields
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    Reviews & endorsements

    "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

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    Product details

    • Date Published: May 2013
    • format: Hardback
    • isbn: 9781107034891
    • length: 286 pages
    • dimensions: 236 x 155 x 19 mm
    • weight: 0.51kg
    • availability: In stock
  • Table of Contents

    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.

  • Author

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

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