Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories

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Auslander-Reiten theory in a Krull-Schmidt category

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 Auslander-Reiten triangle in a triangulated category. We then define the Auslander-Reiten quiver of a Krull-Schmidt category and describe the shapes of its semi-stable components. The main result generalizes those fo...

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ژورنال

عنوان ژورنال: Journal of Pure and Applied Algebra

سال: 2020

ISSN: 0022-4049

DOI: 10.1016/j.jpaa.2019.04.017