We introduce the new concept of silting modules. These modules generalize tilting modules
over an arbitrary ring, as well as support-tilting modules over a finite dimensional algebra …

We study two kinds of reduction processes of triangulated categories, that is, silting
reduction and Calabi–Yau reduction. It is shown that the silting reduction $\mathcal …

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 …

Let be a triangulated category with shift functor. Suppose is a co-t-structure with coheart and
extended coheart, which is an extriangulated category. We show that there is a bijection …

Discrete derived categories were studied initially by Vossieck ['The algebras with discrete
derived category', J. Algebra 243 (2001) 168–176] and later by Bobiński, Geiß and …

We classify compactly generated co-$ t $-structures on the derived category of a
commutative noetherian ring. In order to accomplish this, we develop a theory for compactly …

Recent results by Keller and Nicolás and by Koenig and Yang have shown bijective
correspondences between suitable classes of t-structures and cot-structures with certain …

Let $ Q $ be an acyclic quiver and $ w\geqslant 1$ be an integer. Let $\mathsf {C} _ {-
w}({\mathbf {k}} Q) $ be the $(-w) $-cluster category of ${\mathbf {k}} Q $. We show that there …

Presilting and silting subcategories in extriangulated categories were introduced by Adachi
and Tsukamoto recently, which are generalizations of those concepts in triangulated …

We introduce and study several homological notions which generalise the discrete derived
categories of D. Vossieck. As an application, we show that Vossieck discrete algebras have …