We give an overview of recent developments in silting theory. After an introduction on torsion
pairs in triangulated categories, we discuss and compare different notions of silting and …

In the setting of compactly generated triangulated categories, we show that the heart of a
(co) silting t-structure is a Grothendieck category if and only if the (co) silting object satisfies …

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 …

Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the
derived category D (Mod-R). We determine the simple objects in this heart and their injective …

We prove that, given any strong and stable derivator and a t-structure in its base triangulated
category D, the t-structure canonically lifts to all the (coherent) diagram categories and each …

We study the notions of n-hereditary rings and its connection to the classes of finitely n-
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …

Starting with a Grothendieck category $\mathcal {G} $ and a torsion pair $\mathbf
{t}=(\mathcal {T},\mathcal {F}) $ in $\mathcal G $, we study the local finite presentability and …

Starting with a Grothendieck category G and a torsion pair t D. T; F/in G, we study the local
finite presentability and local coherence of the heart Ht of the associated Happel–Reiten …

Abstract In [16], a theory of universal extensions in abelian categories is developed; in
particular, the notion of Ext 1-universal object is presented. In the present paper, we show …

Approximation theory is a fundamental tool in order to study the representation theory of a
ring R. Roughly speaking, it consists in determining suitable additive or abelian …