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.