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

D. Fuentes-Keuthan, M. Kedziorek and M. Rovelli

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.

Keywords: rederivator, model structure, (∞,1)-category, quasi-category

2010 MSC: 55U35, 18G30, 18A25

Theory and Applications of Categories, Vol. 34, 2019, No. 39, pp 1220-1245.

Published 2019-11-13.


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