Abstract We revisit Auslander–Buchweitz approximation theory and find some relations with
cotorsion pairs and model category structures. From the notion of relative generators, we …

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides
a starting point to study the relationship between homological and homotopical algebra, a …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

We define model structures on exact categories, which we call exact model structures. We
look at the relationship between these model structures and cotorsion pairs on the exact …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

We make a general study of Quillen model structures on abelian categories. We show that
they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have …

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective
modules over an Iwanaga-Gorenstein ring, we present the concept of left and right n …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

Let $ C $ be an abelian category. We show that under certain hypotheses, a cotorsion pair
$(A, B) $ in $ C $ may induce two natural homological model structures on $ Ch (C) $. One …