We introduce the concept of maximal orthogonal subcategories over artin algebras and
orders, and develop higher Auslander-Reiten theory on them. Auslander-Reiten theory …

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

We study Auslander-Reiten theory in proper abelian subcategories of triangulated
categories with a Serre functor. To initiate this, we use approximations of a Serre functor to …

We investigate the structure of certain almost split sequences in $\mathcal {P}(\Lambda) $,
ie, the category of morphisms between projective modules over an Artin algebra $\Lambda …

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 …

Let R be an artin algebra and C an additive subcategory of mod (R). We construct a t-
structure on the homotopy category K−(C) and argue that its heart HC is a natural domain for …

We develop an Auslander-Reiten theory for triangulated categories which is based on
Brown's representability theorem. In a fundamental article [3], Auslander and Reiten …

Auslander-Reiten duality for module categories is generalized to some sufficiently nice
subcategories. In particular, our consideration works for $\mathcal {P}^{<\infty}(\Lambda) …

Let $\Lambda $ be an artin algebra or, more generally, a locally bounded associative
algebra, and $\mathcal {S}(\Lambda) $ the category of all embeddings $(A\subseteq B) …

In Section l we recall some of the features of Frobenius categories in the setup we need. In
particular, we give an Interpretation of the triangles in a Frobenius category in term of exact …