Homotopy theory of higher categories
 Author/Creator
 Simpson, Carlos, 1962
 Language
 English.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2012.
 Physical description
 xviii, 634 p. : ill. ; 24 cm.
 Series
 New mathematical monographs ; 19.
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. [618]629) and index.
 Contents

 Prologue Acknowledgements Part I. Higher Categories: 1. History and motivation 2. Strict ncategories 3. Fundamental elements of ncategories 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 Menriched 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 ncategories and Segal ncategories. A corollary is the construction of higher functor categories which fit together to form the (n+1)category of ncategories. 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.
(source: Nielsen Book Data)  Supplemental links
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Bibliographic information
 Publication date
 2012
 Responsibility
 Carlos Simpson.
 Series
 New mathematical monographs ; 19
 ISBN
 9780521516952 (hardback)
 0521516951 (hardback)