We introduce the concept of maximal (n− 1)-orthogonal subcategories over Artin algebras
and orders, and develop (n+ 1)-dimensional Auslander–Reiten theory on them. We give the …

We study Auslander correspondence from the viewpoint of higher-dimensional analogue of
Auslander–Reiten theory [O. Iyama, Higher dimensional Auslander–Reiten theory on …

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence
between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

We recall several results in Auslander-Reiten theory for finite-dimensional algebras over
fields and orders over complete local rings. Then we introduce $ n $-cluster tilting …

We investigate the Jordan-Hölder property (JHP) in exact categories. First, we show that
(JHP) holds in an exact category if and only if the Grothendieck monoid introduced by …

We give a classification of all exact structures on a given idempotent complete additive
category. Using this, we investigate the structure of an exact category with finitely many …

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 …

We will study the resolution dimension of functorially finite subcategories. The subcategories
with the resolution dimension zero correspond to ring epimorphisms, and rejective …