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Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories (1809.11043v3)
Published 28 Sep 2018 in math.CT and math.RT
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.