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

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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.

Original languageEnglish
JournalJournal of Pure and Applied Algebra
Volume224
Issue1
Pages (from-to)98-124
Number of pages27
ISSN0022-4049
DOIs
Publication statusPublished - Jan 2020
Externally publishedYes

Keywords

  • Auslander-Reiten sequence
  • Auslander-Reiten theory
  • Cluster category
  • Irreducible morphism
  • Krull-Schmidt category
  • Quasi-abelian category

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