The aim of this paper is two-fold. Given a recollement (T′, T, T ″, i*, i*, i!, j!, j*, j*), where
T′, T, T ″are triangulated categories with small coproducts and T is compactly generated …

Let R be any associative ring, na positive integer and X a full subcategory of the category of
R-modules. The monomorphism category S n (X) of X consists of all the objects (X i, φ i) …

Let A be an abelian category and P (A) be the subcategory of A consisting of projective
objects. Let C be a full, additive and self-orthogonal subcategory of A with P (A) a generator …

The relation between the $ n $-recollements of stable categories of Gorenstein projective
modules and the virtual Gorensteinness of algebras are investigated. Let $ A, B $, and $ C …

We introduce compatible bimodules. If M is a compatible A–B-bimodule, then the Gorenstein-
projective modules over algebra Λ=(AM0B) are explicitly described; and if Λ is Gorenstein …

Let R be a ring, Proj be the class of all the projective right R-modules, K be the full
subcategory of the homotopy category K (Proj) whose class of objects consists of all the …

For a finite acyclic quiver Q, an ideal I of a path algebra kQ generated by monomial relations,
and a finite-dimensional k-algebra A, we introduce the separated monic representations of a …

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 …

Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under
extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this …

Let be a class of left R-modules that contains all projective left R-modules. We study a kind
of stability of-Gorenstein projective modules and settle in affirmative the following question …