On higher-dimensional Auslander–Reiten theory for comodule categories
Volume 171 / 2023
Colloquium Mathematicum 171 (2023), 79-101
MSC: Primary 16T15; Secondary 16G70.
DOI: 10.4064/cm8475-12-2021
Published online: 4 July 2022
Abstract
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.
