In this paper, motivated by a τ-tilting version of the Brauer-Thrall Conjectures, we study
general properties of band modules and their endomorphisms in the module category of a …

In this short note, we state a stable and a $\tau $-reduced version of the second Brauer-
Thrall Conjecture. The former is a slight strengthening of a brick version of the second …

For a length abelian category, we show that all torsion-free classes can be classified by
using only the information on bricks, including non functorially-finite ones. The idea is to …

We study two classes of torsion classes which generalize functorially finite torsion classes,
that is, semistable torsion classes and morphism torsion classes. Semistable torsion classes …

In this article we study chains of torsion classes in an abelian category $\mathcal {A} $. We
prove that each chain of torsion classes induce a Harder-Narasimhan filtration for every …

We treat the τ-tilting finiteness of minimal representation-infinite algebras and particularly the
non-distributive ones. Building upon the new results of Bongartz, we fully determine which …

Motivated by a new conjecture on the behavior of bricks, we start a systematic study of
minimal-tilting infinite (min--infinite, for short) algebras. In particular, we treat min--infinite …

The term τ-tilting theory was coined by Adachi, Iyama and Reiten in [1] at the beginning of
the 2010s. In their paper, the authors created a fresh approach to the study of two classical …

A BRICK VERSION OF A THEOREM OF AUSLANDER Page 1 Nagoya Math. J., 249 (2023),
88–106 DOI 10.1017/nmj.2022.22 A BRICK VERSION OF A THEOREM OF AUSLANDER …

Abstract τ-cluster morphism categories, introduced by Buan and Marsh, are a generalization
of cluster morphism categories (defined by Igusa and Todorov). We show the classifying …