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 …

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 …

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 …

Every projective module is flat. Conversely, every flat module is a direct limit of finitely
generated free modules; this was proved independently by Govorov and Lazard in the …

We study the category Rep (Q, M) of representations of a quiver Q with values in an abelian
category M. Under certain assumptions, we show that every cotorsion pair (A, B) in M …

We show that if the given cotorsion pair in the category of modules is complete and
hereditary, then both of the induced cotorsion pairs in the category of complexes are …

In the general setting of Grothendieck categories with enough projectives, we prove
theorems that make possible to restrict the study of the problem of the existence of F-covers …

Abstract We study Gorenstein categories. We show that such a category has Tate
cohomological functors and Avramov–Martsinkovsky exact sequences connecting the …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …