Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective
modules over an Iwanaga-Gorenstein ring, we present the concept of left and right n …

Given a non-negative integer n and a complete hereditary cotorsion triple, the notion of
subcategories in an abelian category is introduced. It is proved that a virtually Gorenstein …

Let 𝒜 be an abelian category and 𝒳, 𝒴, 𝒵 additive full subcategories of 𝒜. We introduce and
study the Gorenstein category 𝒢 (𝒳, 𝒴, 𝒵) as a common generalization of some known …

Since Eilenberg and Moore [EM], the relative homological algebra, especially the
Gorenstein homological algebra ([EJ2]), has been developed to an advanced level. The …

The main objective of this paper is to study the relative derived categories from various
points of view. Let A be an abelian category and C be a contravariantly finite subcategory of …

Let $\A $ be an abelian category, and $\V $, $\W $ two additive full subcategories of $\A $.
We introduce and study the $\V\W $-Gorenstein subcategory of $\A $, which unifies many …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

We introduce the notion of relative singularity category with respect to any self-orthogonal
subcategory $\omega $ of an abelian category. We introduce the Frobenius category of …

We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …