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 …

Higher Auslander’s Formula | International Mathematics Research Notices | Oxford
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Let R be a commutative artinian ring. We extend higher Auslander correspondence from
Artin R-algebras of finite representation type to dualizing R-varieties. More precisely, for a …

For an exact category EE with enough projectives and with ad Z d Z-cluster tilting
subcategory, we show that the singularity category of EE admits ad Z d Z-cluster tilting …

Inspired by the recent work of Henrard, Kvamme and van Roosmalen [17], we prove a
categorified version of higher Auslander correspondence in the context of exact categories …

We study localization theory in higher homological algebra, concentrating at the
localizations of n-abelian and n-angulated categories. In both cases, starting with a class of …

We prove a higher-dimensional version of the Freyd-Mitchell embedding theorem for n-
abelian categories. More precisely, for a positive integer n and a small n-abelian category M …

Let C be an additive category equipped with an automorphism Σ. We show how to obtain n-
angulations of (C, Σ) using some particular periodic injective resolutions. We give necessary …

We show that the category of finitely generated free modules over certain local rings is-
angulated for every. In fact, we construct several classes of-angles, parameterized by …

Let C be an (n+ 2)-angulated category with an n-suspension functor Σ n and X be a cluster-
tilting subcategory of C. Then we show that the quotient category C/X is an n-abelian …