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 Szumiło. We use this comparison result to deduce various abstract properties of the obtained prederivators.

Final version, incorporating suggestions by referee. Accepted for publication in Algebraic & Geometric Topology

References in corpus (3)

• Higher Topos Theory
• Cofibrations in Homotopy Theory
• Two Models for the Homotopy Theory of Cocomplete Homotopy Theories

Cited by in corpus (5)

• Comparison of Waldhausen constructions
• Abstract cubical homotopy theory
• Higher symmetries in abstract stable homotopy theories
• Enriched Derivators
• A model structure on prederivators for $(\infty ,1)$-categories