Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories
Amit Shah
TL;DR
This paper extends Auslander-Reiten theory to semi-abelian, quasi-abelian, and Krull-Schmidt categories, removing previous restrictions and providing new characterizations of Auslander-Reiten sequences.
Contribution
It generalizes Auslander-Reiten theory to broader categorical contexts and removes restrictions like Hom-finiteness and indecomposability.
Findings
Generalization of Auslander-Reiten theory to semi-abelian and quasi-abelian categories
Removal of Hom-finiteness and indecomposability restrictions in Krull-Schmidt categories
Equivalent characterizations of Auslander-Reiten sequences in these categories
Abstract
We generalise some of the theory developed for abelian categories in papers of Auslander and Reiten to semi-abelian and quasi-abelian categories. In addition, we generalise some Auslander-Reiten theory results of S. Liu for Krull-Schmidt categories by removing the Hom-finite and indecomposability restrictions. Finally, we give equivalent characterisations of Auslander-Reiten sequences in a quasi-abelian, Krull-Schmidt category.
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