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 …

Let A be an Artin algebra. As we know, the construction of the well-known Auslander-Reiten
sequence is based on the natural (A, A)-bimodule A and the induced transpose, where the …

We first introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category.
This unifies the notion of an almost split sequence in an abelian category and that of an …

A classical theorem of Zimmermann describes the relation between almost split sequences
in the category of finitely presented modules and those in the category of all modules over …

This paper studies Auslander-Reiten triangles in subcategories of triangulated categories.
The main theorem shows that the Auslander-Reiten triangles in a subcategory are closely …

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) …

This article consists of an introduction to Iyama's higher Auslander–Reiten theory for Artin
algebras from the viewpoint of higher homological algebra. We provide alternative proofs of …

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 …

Generic modules were introduced by Crawley-Boevey in order to provide a better
understanding of finite-dimensional algebras of tame representation type. In fact he has …

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 …