Abstract In n-Exangulated Categories (I), we introduced the notion of n-exangulated
categories for each positive integer n. It is not only a higher dimensional analogue of …

We generalize the notions of n-cluster tilting subcategories and τ-selfinjective algebras into
n-precluster tilting subcategories and τ n-selfinjective algebras, where we show that a …

The symplectic geometry of higher Auslander algebras: Symmetric products of disks Page 1
Forum of Mathematics, Sigma (2021), Vol. 9:e10 1–49 doi:10.1017/fms.2021.2 RESEARCH …

We develop a novel combinatorial perspective on the higher Auslander algebras of type A, a
family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This …

We investigate how to characterize subcategories of abelian categories in terms of intrinsic
axioms. In particular, we find axioms which characterize generating cogenerating functorially …

Abstract In 1996, Edelman and Reiner defined the two higher Stasheff–Tamari orders on
triangulations of cyclic polytopes and conjectured them to coincide. We open up an …

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 …

We study periodicity and twisted periodicity of the trivial extension algebra $ T (A) $ of a finite-
dimensional algebra $ A $. Our main results show that (twisted) periodicity of $ T (A) $ is …

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 …

We investigate the role of gentle algebras in higher homological algebra. In the first part of
the paper, we show that if the module category of a gentle algebra Λ contains ad-cluster …