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

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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
Pages (from-to)98-124
Number of pages27
Publication statusPublished - Jan 2020
Externally publishedYes

Bibliographical note

Funding Information:
The author would like to thank Robert J. Marsh for his helpful guidance and support during the preparation of this article, and also the University of Leeds for financial support through a University of Leeds 110 Anniversary Research Scholarship. The author is grateful to the referee for comments on an earlier version of the paper.

Publisher Copyright:
© 2019

Copyright 2019 Elsevier B.V., All rights reserved.

    Research areas

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

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