| Titre : | Homotopy theory of higher categories : from Segal categories to n-categories and beyond | | Type de document : | texte imprimé | | Auteurs : | Carlos Simpson, Auteur | | Editeur : | Cambridge : Cambridge University Press | | Année de publication : | Cop. 2012 | | Collection : | New mathematical monographs num. 19 | | Importance : | VIII-634 p. | | ISBN/ISSN/EAN : | 978-0-521-51695-2 | | Langues : | Anglais | | Mots-clés : | homotopie catégorie | | Résumé : | 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. | | Note de contenu : | index, références | | En ligne : | http://www.cambridge.org/us/academic/subjects/mathematics/geometry-and-topology/ [...] |
Homotopy theory of higher categories : from Segal categories to n-categories and beyond [texte imprimé] / Carlos Simpson, Auteur . - Cambridge : Cambridge University Press, Cop. 2012 . - VIII-634 p.. - ( New mathematical monographs; 19) . ISBN : 978-0-521-51695-2 Langues : Anglais | Mots-clés : | homotopie catégorie | | Résumé : | 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. | | Note de contenu : | index, références | | En ligne : | http://www.cambridge.org/us/academic/subjects/mathematics/geometry-and-topology/ [...] |
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Affiner la recherche Interroger des sources externesAsymptotic behavior of monodromy / Carlos Simpson (1991)
Homotopy theory of higher categories / Carlos Simpson (Cop. 2012)
