Existence of n-Auslander–Reiten sequences via a finiteness condition

Abstract

Xiao and Zhu proved that if is a locally finite triangulated category, then has Auslander–Reiten triangles. Let n be a positive integer. The notion of n-abelian categories is a higher analogue of abelian categories. In this paper, we introduce the notion of locally finite n-abelian categories and we prove that they admit n-Auslander–Reiten sequences. As an application, we obtain more existence conditions based on results of Auslander on functor categories.