Geodesic
A model structure on prederivators for (∞,1)-categories
Theory and applications of categories, Tome 34 (2019), pp. 1220-1245.

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By theorems of Carlson and Renaudin, the theory of (∞,1)-categories embeds in that of prederivators. The purpose of this paper is to give a two-fold answer to the inverse problem: understanding which prederivators model (∞,1)-categories, either strictly or in a homotopical sense. First, we characterize which prederivators arise on the nose as prederivators associated to quasicategories. Next, we put a model structure on the category of prederivators and strict natural transformations, and prove a Quillen equivalence with the Joyal model structure for quasicategories.
Publié le :
Classification : 55U35, 18G30, 18A25
Keywords: rederivator, model structure, (∞, 1)-category, quasi-category 
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     title = {A model structure on prederivators for (\ensuremath{\infty},1)-categories},
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D. Fuentes-Keuthan; M. Kedziorek; M. Rovelli. A model structure on prederivators for (∞,1)-categories. Theory and applications of categories, Tome 34 (2019), pp. 1220-1245. http://geodesic.mathdoc.fr/item/TAC_2019_34_a38/