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

TL;DR

This paper establishes an equivalence between the homotopy prederivators of cofibration categories and their associated quasi-categories, enabling the transfer of properties and insights between these frameworks.

Contribution

It proves the equivalence of homotopy prederivators for cofibration categories and quasi-categories, providing a new bridge for studying their properties.

Findings

Homotopy prederivator of a cofibration category is equivalent to that of its associated quasi-category.

Derived various abstract properties of the prederivators from this equivalence.

Enhanced understanding of the relationship between 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.