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

Let $\Lambda $ be an Artin algebra and let $ e $ be an idempotent in $\Lambda $. We study
certain functors which preserve the singularity categories. Suppose $\operatorname …

In this paper we continue the study of Artin Schelter regular categories, initiated by the
authors in [7],[8], having in mind applications to the representation theory of finite …

To any additive category, we associate in a functorial way two additive categories A (), B ().
The category A (), resp. B (), is the reflection of in the category of additive categories with …

We study irreducible morphisms in the bounded derived category of finitely generated
modules over an Artin algebra Λ, denoted Db (Λmod), by means of the underlying category …

The theory of morphisms being determined by objects was originally investigated by
Auslander, and can be seen as the culmination part of Auslander-Reiten theory. This theory …

If $\Lambda $ is an artin algebra there is a partition of $\operatorname {ind}\Lambda $, the
category of indecomposable finitely generated $\Lambda $-modules, $\operatorname …

Let A be an artin algebra and modA the category of finitely generated A-modules. Unless
stated to the contrary, by a subcategory C of a category we mean a full subcategory of an …

We give analogues of the Auslander correspondence for two classes of triangulated
categories satisfying certain finiteness conditions. The first class is triangulated categories …

We will study the relationship of quite different objects in the theory of artin algebras, namely
Auslander-regular rings of global dimension two, torsion theories, $\tau $-categories and …