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 …

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 …

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 …

Starting from its original definition in module categories with respect to projective modules,
the index has played an important role in various aspects of homological algebra …

Wide subcategories of 𝑑-cluster tilting subcategories Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 373, Number 4, April 2020, Pages 2281–2309 …

Let Φ be a finite dimensional algebra over an algebraically closed field k and assume gldim
Φ≤ d, for some fixed positive integer d. For d= 1, Brüning proved that there is a bijection …

Nakaoka and Palu introduced the notion of extriangulated categories by extracting the
similarities between exact categories and triangulated categories. In this paper, we study …

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 …