We investigate the (separated) monomorphism category $\operatorname
{mono}(Q,\Lambda) $ of a quiver $ Q $ over an Artin algebra $\Lambda $. We construct an …

We study irreducible morphisms in the bounded derived category of finitely generated
modules over an Artin algebra Λ, denoted Db (Λmod), by means of the underlying category …

We clarify the relation between the subcategory D hf b (A) of homological finite objects in D b
(A) and the subcategory K b (P) of perfect complexes in D b (A), by giving two classes of …

Using the Morita-type embedding, we show that any exact category with enough projectives
has a realization as a (pre) resolving subcategory of a module category. When the exact …

Let Λ be an artin algebra of finite global dimension. We study when the composition of three
irreducible morphisms between indecomposable complexes in K b (proj Λ) is a non-zero …

Abstract Let A, B and C be artin algebras such that there is a recollement of D (Mod A)
relative to D (Mod B) and D (Mod C). We compare the algebras A, B and C with respect to …

We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–
Schmidt exact category 𝒞. This duality induces the generalized Auslander–Reiten …

In this paper, we give a geometric construction of the quantum group using Nakajima
categories, which were developed in Scherotzke ('Quiver varieties and self-injective …

We study necessary and sufficient conditions for the existence of n irreducible morphisms in
the bounded derived category of an Artin algebra, with non-zero composite in the n+ 1 …

In this article we further study the full subcategories of the category of finitely generated
modules over an Artin algebra introduced in Platzeck and Pratti, consisting of the modules …