Higher-dimensional Auslander–Reiten theory on (d+2)-angulated categories

Let \mathscr{C}be a (d+2)-angulated category with d -suspension functor \Sigma^d. Our main results show that every Serre functor on \mathscr{C}is a (d+2)-angulated functor. We also show that \mathscr{C}has a Serre functor \mathbb{S}if and only if \mathscr{C}has Auslander–Reiten (d+2)-angles. Moreover, \tau_d=\mathbb{S}\Sigma^{-d}where \tau_dis d -Auslander–Reiten translation. These results generalize work by...