This paper mainly studies the relative Gorenstein objects in the extriangulated category
$\mathcal {C}=(\mathcal {C},\mathbb {E},\mathfrak {s}) $ with a proper class $\xi $ and the …

This paper looks for Frobenius subcategories, via the separated monomorphism category
$\operatorname {smon}(Q, I,\mathscr {X}) $, and on the other hand, aims to establish an RSS …

Let R be a commutative ring. We show that any complete duality pair gives rise to a theory of
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …

In this paper we study the finiteness of global Gorenstein AC-homological dimensions for
rings, and answer the questions posed by Becerril, Mendoza, Pérez and Santiago. As an …

For $\Lambda $ a selfinjective algebra, and $ Q $ a finite quiver without oriented cycles, the
algebra $\Lambda Q $ is a Gorenstein algebra and the category ${\rm Gproj}\Lambda Q $ of …

Let $ R $ be a ring, $\textrm {Proj} $ be the class of all projective right $ R $-modules,
$\mathcal K $ be the full subcategory of the homotopy category $\mathbf K (\textrm {Proj}) …

Let XX be a resolving subcategory of an abelian category. In this paper we investigate the
singularity category D_ sg (X)= D^ b (mod\, X)/K^ b (proj (mod\, X)) D sg (X ̲)= D b (mod X …

Let T be a right exact functor from an abelian category B into another abelian category A.
Then there exists an abelian category, named comma category and denoted by (T↓ A). In …

Assume that the class of all Gorenstein (ℒ, 𝒜)-flat modules is closed under extensions. We
define a notion of Gorenstein (ℒ, 𝒜)-flat dimension for complexes and consider equivalent …

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