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Globular perspective for Grothendieck ∞topos and Grothendieck (∞,n)topos
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Formale Metadaten
Titel  Globular perspective for Grothendieck ∞topos and Grothendieck (∞,n)topos 
Serientitel  Topos à l'IHES 
Teil  01 
Anzahl der Teile  28 
Autor 
Kachour, Camell

Lizenz 
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DOI  10.5446/20739 
Herausgeber  Institut des Hautes Études Scientifiques (IHÉS) 
Erscheinungsjahr  2016 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Mathematik 
Abstract  In this short talk we first briefly recall how to build, for each integers n0, monads Tn on the category Glob of globular sets which algebras are globular models of (1; n)categories, which have the virtue to be weak 1categories of Penon and thus also to be weak 1categories of Batanin. On the other hand we are also briefly explain how the difficult problem to prove the existence of the weak higher category of the weak higher categories on the globular setting can be replaced by a very precise technical problem, on the level of globular operads in Batanin’s sense. In the conclusion of the thesis we give some general pictures of how to define right and left weak higher adjunctions for weak higher functors, and also weak higher (co)limits for weak 1 higher functors, by using globular operads. According to an easy characterisation of Grothendieck topos (by using presheaves on a small category), we finish our talk by sketching mains tools which permit to build globular models of Grothendieck 1topos and Grothendieck (1; n)topos (by using weak higher prestacks on a small category). 