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
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
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