On higher-dimensional Auslander–Reiten theory for comodule categories

We introduce the concepts of higher-dimensional defect functors and $n$-Auslander–Reiten translations. Then we prove the higher-dimensional Auslander’s defect formula for the category of finitely $n$-copresented comodules over a left semiperfect coalgebra. Based on this formula, we obtain the higher-dimensional Auslander–Reiten formula for comodule categories.