Theories homotopiques de Quillen combinatoires et derivateurs de Grothendieck

TL;DR

This paper develops a pseudo-localization of combinatorial Quillen model categories and demonstrates its embedding into a 2-category of Grothendieck derivators, advancing the understanding of their categorical relationships.

Contribution

It introduces a pseudo-localization construction for combinatorial Quillen model categories and establishes an embedding into Grothendieck derivators, linking two important categorical frameworks.

Findings

Pseudo-localization of combinatorial Quillen model categories constructed.

Embedding of the pseudo-localization into a 2-category of Grothendieck derivators verified.

Provides a new perspective on the relationship between model categories and derivators.

Abstract

We construct a pseudo-localization of the 2-category of combinatorial Quillen model categories with respect to Quillen equivalences, and then verify that it embeds in a 2-category of Grothendieck derivators.