Homotopy Theory of Higher Categories

From Segal Categories to n-Categories and Beyond

AvCarlos Simpson

Inbunden, Engelska, 2011

Del 19 i serien New Mathematical Monographs

1 060 kr

Beställningsvara. Skickas inom 7-10 vardagar. Fri frakt över 249 kr.

Beskrivning

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.

Produktinformation

Utgivningsdatum:2011-10-20
Mått:158 x 235 x 38 mm
Vikt:1 050 g
Format:Inbunden
Språk:Engelska
Serie:New Mathematical Monographs
Antal sidor:652
Förlag:Cambridge University Press
ISBN:9780521516952

Utforska kategorier

Topologi inom Naturvetenskap och teknik

Mer om författaren

Carlos Simpson is Directeur de Recherche in the CNRS in Toulouse and Nice, France.

Innehållsförteckning

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.