In this paper, we prove a version of Freyd's generating hypothesis for triangulated
categories: if D is a cocomplete triangulated category and S∈ D is an object whose …

For any ring AA and a small, pre‐additive, Hom‐finite, and locally bounded category QQ that
has a Serre functor and satisfies the (strong) retraction property, we show that the category …

We explore the interplay between t‐structures in the bounded derived category of finitely
presented modules and the unbounded derived category of all modules over a coherent ring …

Abstract Beilinson, Bernstein and Deligne introduced the notion of a t-structure on a
triangulated category in [BBD82], with the intended goal to axiomatise the main properties of …

We show that Krause's recollement exists for any locally coherent Grothendieck category
whose derived category is compactly generated. As a source of such categories, we …

Aim: A torsion pair in an abelian category is a decomposition of it into two parts: a torsion
and a torsionfree part. It turns out that both the study of individual torsion pairs and the study …

We study the $ t $-structure induced by an $ n $-tilting module $ T $ in the derived category
$\mathcal {D}(R) $ of a ring $ R $. Our main objective is to determine when the heart of the …

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 …

In this chapter, the reader will become familiar with our notation and basic assumptions on
the one hand; on the other, they are invited to various instances where the setting of Ring …

We construct an" almost involution" assigning a new DG-category to a given one, and use
this construction in order to recover, say, the abelian category of graded modules over the …