Higher-dimensional Auslander–Reiten theory on (<i>d</i>+2)-angulated categories

Abstract Let $\mathscr{C}$ be a $(d+2)$ -angulated category with d -suspension functor $\Sigma^d$ . Our main results show that every Serre on is functor. We also has $\mathbb{S}$ if and only Auslander–Reiten -angles. Moreover, $\tau_d=\mathbb{S}\Sigma^{-d}$ where $\tau_d$ -Auslander–Reiten translation. These generalize work by Bondal–Kapranov Reiten–Van den Bergh. As an application, we prove for strongly functorially finite subcategory $\mathscr{X}$ of , the quotient $\mathscr{C}/\mathscr{X}$ $(\mathscr{C},\mathscr{C})$ -mutation pair, $\tau_d\mathscr{X} =\mathscr{X}$