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 …

Given a right exact functor from an abelian category into another abelian category, there is
an associated abelian category called the comma category of the functor. In this paper, we …

In this paper, we study the relationship of Gorenstein projective objects among three Abelian
categories in a recollement. As an application, we introduce the relation of $ n $-Gorenstein …

We construct a flat model structure on the category $ _ {\mathcal {Q}, R}{\mathsf {Mod}} $ of
additive functors from a small preadditive category $\mathcal {Q} $ satisfying certain …

Let $(\mathcal {C},\mathbb {E},\mathfrak {s}) $ be an extriangulated category with a proper
class $\xi $ of $\mathbb {E} $-triangles. In this paper, we study Gorenstein derived functors …

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 …

Let T be a triangulated category with a proper class ξ of triangles. We introduce the notions
of left Frobenius pairs, left (n-) cotorsion pairs and left (weak) Auslander-Buchweitz contexts …

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) …

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 …

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. In this paper, we first …