A model structure on prederivators for $(\mathrm{\infty },1)$-categories

By theorems of Carlson and Renaudin, the theory of $(\mathrm{\infty },1)$-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 $(\mathrm{\infty },1)$-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.