In this survey article we propose the notion of a bound quiver for an exact category
generalising the classical concept of the Gabriel quiver and its relation for a module …

We investigate the (separated) monomorphism category $\operatorname
{mono}(Q,\Lambda) $ of a quiver $ Q $ over an Artin algebra $\Lambda $. We construct an …

In this paper we systematically consider representations over diagrams of abelian
categories, which unify quite a few notions appearing widely in literature such as …

Let A be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated
Gorenstein projective Λ-modules. In this paper, we study the components of the stable …

Representations over diagrams of abelian categories unify quite a few notions appearing
widely in literature such as representations of categories, presheaves of modules over …

In this article we study the properties of preprojective algebras of representation finite
species. To understand the structure of a preprojective algebra, one often studies its …

In this paper, we introduce multi-layer quiver and show how to construct an $(n+ 1) $-slice
algebras of infinite type from an $ n $-slice algebra of infinite type using the bound quivers …

A well-known theorem of Buchweitz provides equivalences between three categories: the
stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy …

In this paper, we study resolving subcategories and singularity categories. First, if the left
perpendicular category of a module T over an Artin algebra A is the additive closure of …