We study IE-closed subcategories of a module category, subcategories which are closed
under taking Images and Extensions. We investigate the relation between IE-closed …

Abstract We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with
a basic rigid object T, and show a bijection between the set of isomorphism classes of basic …

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 …

In this paper, we study ICE-closed (= Image-Cokernel-Extension-closed) subcategories of
an abelian length category using torsion classes. To each interval [U, T] in the lattice of …

We introduce image-cokernel-extension-closed (ICE-closed) subcategories of module
categories. This class unifies both torsion classes and wide subcategories. We show that …

Abstract Let E=(A, S) be an exact category with enough projectives P. We introduce the
notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of …

A length category ce is an abelian category in which all objects have finite length. It is called
hereditary, provided Exe vanishes everywhere. Since a length category with only a set of …

Let be an extriangulated category with enough projectives P \mathcalP and enough
injectives I \mathcalI, and let be a contravariantly finite rigid subcategory of which contains P …

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 …

Using the Morita-type embedding, we show that any exact category with enough projectives
has a realization as a (pre) resolving subcategory of a module category. When the exact …