An introduction to higher Auslander-Reiten theory

This article consists of an introduction to Iyama's higher Auslander–Reiten theory for Artin algebras from the viewpoint of higher homological algebra. We provide alternative proofs of the basic results in higher Auslander–Reiten theory, including the existence of d-almost-split sequences in d-cluster-tilting subcategories, following the approach to classical Auslander–Reiten theory due to Auslander, Reiten, and Smalø. We show that Krause's proof of Auslander's defect formula can be adapted to give a new proof of the defect formula for d-exact sequences. We use the defect formula to establish the existence of morphisms determined by objects in d-cluster-tilting subcategories.