For a finite‐dimensional algebra A, we establish correspondences between torsion classes
and wide subcategories in mod (A). In case A is representation finite, we obtain an explicit …

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 …

There are well-known constructions relating ring epimorphisms and tilting modules. The new
notion of silting module provides a wider framework for studying this interplay. To every …

Extriangulated categories were introduced by Nakaoka and Palu by extracting the
similarities between exact categories and triangulated categories. A notion of homotopy …

Gentle and Todorov proved that in an abelian category with enough projective objects, the
extension subcategory of two covariantly finite subcategories is covariantly finite. We give an …

As a generalization of a consistent pair of t-structures on triangulated categories, we
introduced the notion of a consistent pair of s-torsion pairs in the extriangulated setup. Let …

Gentle and Todorov proved that in an abelian category with enough projective objects, the
extension subcategory of two covariantly finite subcategories is covariantly finite. We prove a …

This thesis studies faithfully balanced modules, which are faithful modules with the double
centralizer property, and their relative version. For finite-dimensional algebras our main tool …