Gluing and lifting exact model structures for the recollement of exact categories

TL;DR

This paper develops a method to glue hereditary exact model structures in exact categories using cotorsion pairs, enabling the construction of recollements of triangulated categories with applications to various derived and stable categories.

Contribution

It introduces an explicit procedure for gluing hereditary exact model structures via cotorsion pairs and extends recollements to their homotopy categories, providing new tools for triangulated categories.

Findings

Constructed recollements of triangulated categories from exact categories.

Applied the method to contraderived and Gorenstein injective module categories.

Provided a new approach to produce recollements in homotopy categories.

Abstract

In this paper, we first provide an explicit procedure to glue together hereditary exact model structures for the recollement of exact categories. To that end, we use the notion of cotorsion pairs and we investigate the gluing of complete hereditary cotorsion pairs along the recollement of exact categories. Moreover, we study liftings of recollements of hereditary exact model structures to recollements of their associated homotopy categories. This leads to a new method to produce recollements of triangulated categories. Applications are given to contraderived categories, projective stable derived categories and stable categories of Gorenstein injective modules over an upper triangular matrix ring.