We investigate relative cohomology functors on subcategories of abelian categories via
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …

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 …

Gorenstein derived categories are defined, and the relation with the usual derived
categories is given. The bounded Gorenstein derived categories of Gorenstein rings and of …

It is an old observation of Eckmann-Hilton [21], that the homotopy theory of topological
spaces has an algebraic analogue in the module category of a ring. Inspired by the work of …

We study the homotopy category of unbounded complexes with bounded homologies and
its quotient category by the homotopy category of bounded complexes. In the case of the …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

Given an artin algebra $\Lambda $ with an idempotent element $ a $ we compare the
algebras $\Lambda $ and $ a\Lambda a $ with respect to Gorensteinness, singularity …

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 …

The monomorphism category S n (X) is introduced, where X is a full subcategory of the
module category A-mod of an Artin algebra A. The key result is a reciprocity of the …

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 …