Historically, the study of modules over finite dimensional algebras has started with the study
of the ones with finite dimension. This is sufficient when dealing with a finite dimensional …

Let (X, OX) be a noetherian formal scheme and consider D qct (X) its derived category of
sheaves with quasi-coherent torsion homology. We show that there is a bijection between …

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 …

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 …

The paper contains a collection of results related to weight structures, $ t $-structures, and
(more generally) to torsion pairs. For any weight structure $ w $ we study (co) homological …

We systematically develop, study, and give applications of definable functors between
compactly generated triangulated categories. Such functors preserve pure triangles, pure …

It is a well established fact that the notions of quasi-abelian categories and tilting torsion
pairs are equivalent. This equivalence fits in a wider picture including tilting pairs of $ t …

For a commutative ring $ R $, we exploit localization techniques and point-free topology to
give an explicit realization of both the Zariski frame of $ R $(the frame of radical ideals in $ R …

We analyze Auslander-Reiten quivers of functorially finite resolving subcategories. Chapter
1 gives a short introduction into the basic definitions and theorems of Auslander-Reiten …

1.1. Generalities. The present work deals with the following problem. Let R be an associative
ring, and Mod-R the category of all right R-modules. Given a torsion pair (X, Y) in Mod-R …