Model structure arising from one hereditary complete cotorsion pair on extriangulated categories

TL;DR

This paper generalizes Hovey's correspondence between model structures and cotorsion pairs to extriangulated categories using a single hereditary cotorsion pair, and introduces methods to construct model structures from silting objects and co-t-structures.

Contribution

It extends the correspondence to extriangulated categories with one hereditary cotorsion pair, unifying previous work and providing new construction methods.

Findings

Established a generalized correspondence in extriangulated categories.

Provided methods to construct model structures from silting objects.

Linked co-t-structures with model structures in triangulated categories.

Abstract

Hovey's correspondence between model structures and cotorsion pairs in the setting of abelian categories, has been generalized by Nakaoka-Palu, using two cotorsion pairs, to the setting of weakly idempotent complete extriangulated categories, and the aim of the paper is to give an analogous correspondence using one (hereditary) cotorsion pair generalizing in this setting work of Beligiannis-Reiten and Cui, Lu and Zhang. Furthermore, we provide methods to construct model structures from silting objects in weakly idempotent complete extriangulated categories and co-$t$-structures on triangulated categories.