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

Abstract

Let $\mathcal{C}$ be an $n$-exangulated category. In this note, we show that if $\mathcal{C}$ is locally finite, then $\mathcal{C}$ 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.

18 pages. arXiv admin note: substantial text overlap with arXiv:2109.12954; text overlap with arXiv:2108.07985, arXiv:2109.00196. text overlap with arXiv:2006.02223, arXiv:2011.00729, arXiv:1909.13284; text overlap with arXiv:1709.06689 by other authors