We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

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

We show that Quillenʼs small object argument works for exact categories under very mild
conditions. This has immediate applications to cotorsion pairs and their relation to the …

Given a locally coherent Grothendieck category G, we prove that the homotopy category of
complexes of injective objects (also known as the coderived category of G) is compactly …

For a locally presentable abelian category B with a projective generator, we construct the
projective derived and contraderived model structures on the category of complexes …

A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose …

In this paper, we examine the class of K-absolutely pure complexes. These are the
complexes which are right orthogonal in the homotopy category K (R) to the acyclic …

We provide a criterion for the existence of right approximations in cocomplete additive
categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is …

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

The paper is devoted to study some of the questions arises naturally in connection to the
notion of relative derived categories. In particular, we study invariants of recollements …