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Homotopy Theory of Higher Categories

Homotopy Theory of Higher Categories
From Segal Categories to n-Categories and Beyond

$84.99

Part of New Mathematical Monographs

  • Author: Carlos Simpson, Centre National de la Recherche Scientifique (CNRS), Paris
  • Date Published: October 2011
  • availability: Available
  • format: Hardback
  • isbn: 9780521516952

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  • The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.

    • Proposes a working theory of higher categories
    • Focuses on one specific approach based closely on the work of Graeme Segal
    • Useful reference to the different approaches adopted by researchers
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    Product details

    • Date Published: October 2011
    • format: Hardback
    • isbn: 9780521516952
    • length: 652 pages
    • dimensions: 235 x 158 x 38 mm
    • weight: 1.04kg
    • contains: 35 b/w illus.
    • availability: Available
  • Table of Contents

    Prologue
    Acknowledgements
    Part I. Higher Categories:
    1. History and motivation
    2. Strict n-categories
    3. Fundamental elements of n-categories
    4. The need for weak composition
    5. Simplicial approaches
    6. Operadic approaches
    7. Weak enrichment over a Cartesian model category: an introduction
    Part II. Categorical Preliminaries:
    8. Some category theory
    9. Model categories
    10. Cartesian model categories
    11. Direct left Bousfield localization
    Part III. Generators and Relations:
    12. Precategories
    13. Algebraic theories in model categories
    14. Weak equivalences
    15. Cofibrations
    16. Calculus of generators and relations
    17. Generators and relations for Segal categories
    Part IV. The Model Structure:
    18. Sequentially free precategories
    19. Products
    20. Intervals
    21. The model category of M-enriched precategories
    22. Iterated higher categories
    Part V. Higher Category Theory:
    23. Higher categorical techniques
    24. Limits of weak enriched categories
    25. Stabilization
    Epilogue
    References
    Index.

  • Author

    Carlos Simpson, Centre National de la Recherche Scientifique (CNRS), Paris
    Carlos Simpson is Directeur de Recherche in the CNRS in Toulouse and Nice, France.

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