The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

Let $\mathcal B $ be an extriangulated category with enough projectives and enough
injectives. We define a proper $ m $-term subcategory $\mathcal G $ on $\mathcal B …

Abstract Recently, Adachi, Iyama and Reiten [1] introduced support τ-tilting modules which is
an interesting generalization of classical tilting modules and showed that they have close …

Let T be a Krull–Schmidt, Hom-finite triangulated category with suspension functor [1]. Let R
be a basic rigid object, Γ the endomorphism algebra of R, and pr (R)⊆ T the subcategory of …

Throughout the paper A will denote an artin algebra and mod A will denote the category of
finitely generated A-modules. Recently, subcategories of mod A which are the torsion free …

Approximation sequences and derived equivalences occur frequently in the research of
mutation of tilting objects in representation theory, algebraic geometry and noncommutative …

Relative cotilting modules and their connection to ordinary cotilting modules were first
studied by Auslander and Solberg in [6] and [7]. Among other things, they show that relative …

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 propose a new approach to study the relation between the module categories of a tilted
algebra C and the corresponding cluster-tilted algebra B= C⋉ E. This new approach …

We prove that a finite dimensional algebra is τ-tilting finite if and only if it does not admit
large silting modules. Moreover, we show that for a τ-tilting finite algebra A there is a …