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Homotopy theory of higher categories / Carlos Simpson.



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Simpson, Carlos, 1962-
Publication date:
Cambridge, UK ; New York : Cambridge University Press, 2012.
  • Book
  • xviii, 634 p. : ill. ; 24 cm.
Includes bibliographical references (p. [618]-629) and index.
  • Machine generated contents note: 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.
"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"-- Provided by publisher.
New mathematical monographs ; 19.

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