Geodesic
Coherent Nerves for Higher Quasicategories
Theory and applications of categories, Tome 37 (2021), pp. 709-817

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We introduce, for C a regular Cartesian Reedy category a model category whose fibrant objects are an analogue of quasicategories enriched in simplicial presheaves on C. We then develop a coherent realization and nerve for this model structure and demonstrate that these give a Quillen equivalence, in particular recovering the classical one in the process. We then demonstrate that this equivalence descends to any Cartesian closed left Bousfield localization in a natural way. As an application, we demonstrate a version of Yoneda's lemma for quasicategories enriched in any such Cartesian closed localization.

Publié le :
Classification : 18A30, 18D05, 18E35, 18G55, 55P10, 55U35
Keywords: enriched categories, higher category theory, homotopy theory 
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     author = {Harry Gindi},
     title = {Coherent {Nerves} for {Higher} {Quasicategories}},
     journal = {Theory and applications of categories},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2021_37_a22/}
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Harry Gindi. Coherent Nerves for Higher Quasicategories. Theory and applications of categories, Tome 37 (2021), pp. 709-817. http://geodesic.mathdoc.fr/item/TAC_2021_37_a22/