Let $ k $ be a commutative ring, let ${\mathcal {C}} $ be a small, $ k $-linear, Hom-finite,
locally bounded category, and let ${\mathcal {B}} $ be a $ k $-linear abelian category. We …

We introduce the right (left) Gorenstein subcategory relative to an additive subcategory CC
of an abelian category AA, and prove that the right Gorenstein subcategory rG (G (C) G (C)) …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

We apply previous techniques on infinite quivers to describe projective and injective
modules over a monomial algebra Λ= RQ/I (where R is any arbitrary ring with identity). Then …

We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

Let A be a finite-dimensional Gorenstein algebra of finite CM-type. We show that the
Gorenstein derived category of A has Auslander–Reiten triangles. In this case, we otain a …

Given an additive category C and an integer n⩾ 2. We form a new additive category C [ϵ] n
consisting of objects X in C equipped with an endomorphism ϵ X satisfying ϵ X n= 0. First …

The aim of this paper is to introduce Gorenstein singularity category D gpsgb (A), as the
Verdier quotient of the Gorenstein derived category D gpb (A) by the triangulated …

In this paper we characterize when the path ring associated to a quiver is Gorenstein (in the
sense of Iwanaga [9]). Then, by using the notion of a Gorenstein category (cf.[2]), we extend …