Open Access
October 2022 On the existence of Auslander–Reiten $n$-exangles in $n$-exangulated categories
Jian He, Jiangsheng Hu, Dongdong Zhang, Panyue Zhou
Author Affiliations +
Ark. Mat. 60(2): 365-385 (October 2022). DOI: 10.4310/ARKIV.2022.v60.n2.a8

Abstract

Let $\mathscr{C}$ be an $n$-exangulated category. In this note, we show that if $\mathscr{C}$ is locally finite, then $\mathscr{C}$ has Auslander–Reiten $n$-exangles. This unifies and extends results of Xiao–Zhu, Zhu–Zhuang, Zhou, and Xie–Lu–Wang for triangulated, extriangulated, $(n+2)$-angulated and $n$-abelian categories, respectively.

Funding Statement

Jian He was supported by the National Natural Science Foundation of China (Grant No. 12171230).
Jiangsheng Hu was supported by the NSF of China (Grant Nos. 12171206 and 12126424), the Natural Science Foundation of Jiangsu Province (Grant No. BK20211358), and Jiangsu 333 Project.

Citation

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Jian He. Jiangsheng Hu. Dongdong Zhang. Panyue Zhou. "On the existence of Auslander–Reiten $n$-exangles in $n$-exangulated categories." Ark. Mat. 60 (2) 365 - 385, October 2022. https://doi.org/10.4310/ARKIV.2022.v60.n2.a8

Information

Received: 27 October 2021; Accepted: 19 January 2022; Published: October 2022
First available in Project Euclid: 17 July 2024

Digital Object Identifier: 10.4310/ARKIV.2022.v60.n2.a8

Keywords: $n$-abelian categories , $n$-exangulated categories , Auslander–Reiten $n$-exangles , extriangulated categories , locally finite , triangulated categories

Rights: Copyright © 2022 Institut Mittag-Leffler

Vol.60 • No. 2 • October 2022
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