TY - JOUR
T1 - Auslander-Reiten theory in quasi-abelian and Krull-Schmidt categories
AU - Shah, Amit
N1 - 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:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2020/1
Y1 - 2020/1
N2 - 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.
AB - 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.
KW - Auslander-Reiten sequence
KW - Auslander-Reiten theory
KW - Cluster category
KW - Irreducible morphism
KW - Krull-Schmidt category
KW - Quasi-abelian category
UR - http://www.scopus.com/inward/record.url?scp=85064711859&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2019.04.017
DO - 10.1016/j.jpaa.2019.04.017
M3 - Journal article
AN - SCOPUS:85064711859
SN - 0022-4049
VL - 224
SP - 98
EP - 124
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1
ER -