Let $\mathcal {A} $ be a small dg category over a field $ k $ and let $\mathcal {U} $ be a
small full subcategory of the derived category $\mathcal {D}\mathcal {A} $ which generates …

We consider an arbitrary Abelian category A and a subcategory T closed under extensions
and direct summands, and characterize those T that are (semi-) special preenveloping in A; …

In a compactly generated triangulated category, we introduce a class of tilting objects
satisfying a certain purity condition. We call these the decent tilting objects and show that the …

Given a noetherian abelian k-category of finite homological dimension, with a tilting object T
of projective dimension 2, the abelian category and the abelian category of modules over …

Let $\mathcal C $ be a Krull-Schmidt triangulated category with shift functor $[1] $ and
$\mathcal R $ be a rigid subcategory of $\mathcal C $. We are concerned with the mutation …

We introduce the notion of big tilting complexes over associative rings, which is a
simultaneous generalization of good tilting modules and tilting complexes over rings. Given …

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 …

An algebra is said to be-tilting finite provided it has only a finite number of-rigid objects up to
isomorphism. To each such algebra, we associate a category whose objects are the wide …

Extriangulated categories give a simultaneous generalization of triangulated categories and
exact categories. In this paper, we study silting subcategories of an extriangulated category …

In this paper, we study ICE-closed (= Image-Cokernel-Extension-closed) subcategories of
an abelian length category using torsion classes. To each interval [U, T] in the lattice of …