Higher Auslander-Reiten sequences revisited

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an $n$-exangulated category with enough projectives and enough injectives, and $\mathcal{X}$ be a cluster-tilting subcategory of $\mathcal{C}$. Liu and Zhou have shown that the quotient category $\mathcal{C}\mathrm{/}\mathcal{X}$ is an $n$-abelian category. In this paper, we prove that if $\mathcal{C}$ has Auslander-Reiten $n$-exangles, then $\mathcal{C}\mathrm{/}\mathcal{X}$ has Auslander-Reiten $n$-exact sequences. Moreover, we also show that if a Frobenius $n$-exangulated category $\mathcal{C}$ has Auslander-Reiten $n$-exangles, then the stable category $\bar{\mathcal{C}}$ of $\mathcal{C}$ has Auslander-Reiten $(n+2)$-angles.