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A model structure on prederivators for (∞,1)-categories

2018/10/15 by Fuentes-Keuthan, Daniel, Kedziorek, Magdalena, Rovelli, Martina
#18A25 #18G30 #55U35 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.06496

Abstract

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.

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