Prederivators as a model of (∞,1)-categories

By theorems of Carlson and Renaudin, the theory of (∞,1)-categories embeds in that of prederivators. We present two approaches to address the inverse problem: understanding which prederivators model (∞,1)-categories. First, we put a model structure on the category of prederivators that is Quillen equivalent to the Joyal model structure for quasi-categories. Second, we give an intrinsic description of which prederivators arise on the nose as prederivators associated to quasi-categories. This is joint work with D. Fuentes-Keuthan and M. Kędziorek.