An extension $ B\subset A $ of finite dimensional algebras is bounded if the $ B $-$ B $-
bimodule $ A/B $ is $ B $-tensor nilpotent, its projective dimension is finite and $\mathrm …

We make a general study of Quillen model structures on abelian categories. We show that
they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have …

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 …

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 …

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 …

Abstract We study Gorenstein categories. We show that such a category has Tate
cohomological functors and Avramov–Martsinkovsky exact sequences connecting the …

From certain triangle functors, called nonnegative functors, between the bounded derived
categories of abelian categories with enough projective objects, we introduce their stable …

In this paper we construct Gorenstein-projective modules over Morita rings with zero
bimodule homomorphisms and we provide sufficient conditions for such rings to be …

ABSTRACT A natural generalization of locally noetherian and locally coherent categories
leads us to define locally type FP∞ categories. They include not just all categories of …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …