Homotopy (Pre-)Derivators of Cofibration Categories and Quasi-Categories

Abstract

We prove that the homotopy prederivator of a cofibration category is equivalent to the homotopy prederivator of its associated quasi-category of frames, as introduced by Szumi\l{}o. We use this comparison result to deduce various abstract properties of the obtained prederivators.Comment: Final version, incorporating suggestions by referee. Accepted for publication in Algebraic & Geometric Topolog