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

31 pages, to appear in Journal of Pure and Applied Algebra (available online: https://doi.org/10.1016/j.jpaa.2019.04.017)

References in corpus (2)

• On triangulated orbit categories
• Quasi-abelian hearts of twin cotorsion pairs on triangulated categories

Cited by in corpus (11)

• Auslander's formula and correspondence for exact categories
• The category of extensions and a characterisation of $n$-exangulated functors
• On the existence of Auslander-Reiten (d+2)-angles in (d+2)-angulated categories
• Grothendieck groups in extriangulated categories
• Quasi-abelian hearts of twin cotorsion pairs on triangulated categories
• Continuous Quivers of Type A (II) The Auslander-Reiten Space
• Idempotent completions of $n$-exangulated categories
• Higher Auslander-Reiten sequences via morphisms determined by objects
• Largest exact structures and almost split sequences on hearts of twin cotorsion pairs
• Auslander-Reiten-Serre duality for n-exangulated categories
• Stratifying systems and Jordan-Hölder extriangulated categories