Left determined model structures for locally presentable categories

TL;DR

This paper generalizes Cisinski's construction of cofibrantly generated model structures from toposes to locally presentable categories, broadening the scope and establishing conditions for these structures to be 'left determined' as per Rosicky and Tholen.

Contribution

It extends the construction of cofibrantly generated model structures to a wider class of categories and generalizes the types of cofibrations considered, under new conditions.

Findings

Model structures can be constructed on locally presentable categories.

The generalized model structures are 'left determined' under certain conditions.

The work broadens the applicability of Cisinski's results to more categories.

Abstract

We extend a result of Cisinski on the construction of cofibrantly generated model structures from (Grothendieck) toposes to locally presentable categories and from monomorphism to more general cofibrations. As in the original case, under additional conditions, the resulting model structures are "left determined" in the sense of Rosicky and Tholen.