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 prove a generalization of the stability for Gorenstein categories in [36] and [24]; and
show that the relative Auslander algebra of a CM-finite algebra is CM-free. On the other …

Let 𝒜 be an abelian category having enough projective and injective objects, and let 𝒯 be
an additive subcategory of 𝒜 closed under direct summands. A known assertion is that in a …

Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a
finite-dimensional self-injective algebra is projective. This conjecture is an important part of …

Abstract Let (C, E, s C, E, s) be an extriangulated category with a proper class ξ of E E-
triangles, and WW an additive full subcategory of (C, E, s C, E, s). We provide a method for …

For any exact category A with splitting idempotents, a maximal exact category T (A)
containing A as a biresolving subcategory, is constructed. Important types of exact …

We introduce relative preresolving subcategories and precoresolving subcategories of an
abelian category and define homological dimensions and codimensions relative to these …

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 …

The paper is devoted to study some of the questions arises naturally in connection to the
notion of relative derived categories. In particular, we study invariants of recollements …

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)) …