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On the existence of Auslander-Reiten $n$-exangles in $n$-exangulated categories (2110.02476v1)
Published 6 Oct 2021 in math.RT and math.CT
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.