We generalize Ringel and Schmidmeier's theory on the Auslander–Reiten translation of the
submodule category 𝒮 2 (A) to the monomorphism category 𝒮 n (A); the category consists of …

If H is a hereditary abelian category with tilting object, then it is shown that H is derived
equivalent to a module category over a hereditary artin algebra provided H contains a …

Let A be a essentially small abelian category and C be a Serre subcategory of A. Consider
the quotient functor q: A→ A/C. For an object A∈ A and a non-negative integer k we …

Quasi-hereditary algebras were introduced by E. Cline, B. Parshall and L. Scott in order to
deal with highest weight categories as they arise in the representation theory of semi-simple …

While homological algebra has been used extensively in the representation theory of artin
algebras, relative homological algebra has been used only sporadically. It is our hope that …

Let $(\mbox {mod}\Lambda',\mbox {mod}\Lambda,\mbox {mod}\Lambda'') $ be a recollement
of abelian categories for artin algebras $\Lambda'$, $\Lambda $ and $\Lambda''$. Under …

Let Λ be an Artin algebra and be an object in, the morphism category of Λ. We will describe
the Auslander–Reiten translate of, ie, as an object in. It is shown that, even though there may …

In this paper we continue the project of generalizing tilting theory to the category of
contravariant functors $ Mod (C) $, from a skeletally small preadditive category $ C $ to the …

We study sufficient conditions for a morphism in the category of complexes of fixed size C n
(proj A), with n≥ 2 and A an artin algebra, to belong to the infinite radical of K−, b (proj A). As …

Let A be a quasi-hereditary algebra. The aim of this paper is to show that the category of all
A-modules with good filtrations is functorially finite in A-mod, thus it has (relative) almost split …