On the existence of Auslander–Reiten $n$-exangles in $n$-exangulated categories
On the existence of Auslander–Reiten $n$-exangles in $n$-exangulated categories
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DOI：
10.4310/arkiv.2022.v60.n2.a8
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发表时间：
2021-10
期刊：
影响因子：
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通讯作者：
Jian He;Jiangsheng Hu;Dongdong Zhang;Panyue Zhou
中科院分区：
文献类型：
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作者：
Jian He;Jiangsheng Hu;Dongdong Zhang;Panyue Zhou
设$\mathscr{C}$是一个$n$-换角范畴。在本文中，我们证明了如果$\mathscr{C}$是局部有限的，则$\mathscr{C}$有Auslander-Reiten $n$-可换角。这统一和推广了Xiao-Zhu，Zhu-Zhuang，Zhou和Xie-Lu-Wang分别关于三角范畴，外三角范畴，$（n+2）$-angulated范畴和$n$-abel范畴的结果.
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.