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arXiv · 2110.02476

On the existence of Auslander-Reiten $n$-exangles in $n$-exangulated categories

Jian He·Jiangsheng Hu·Dongdong Zhang·Panyue Zhou
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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.

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Jian He, Jiangsheng Hu, Dongdong Zhang, Panyue Zhou. 2021-10-06. On the existence of Auslander-Reiten $n$-exangles in $n$-exangulated categories. https://arxiv.org/abs/2110.02476

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