Semibricks and the Jordan–Hölder property

Abstract

Let [Formula: see text] be an extriangulated category and [Formula: see text] be a semibrick in [Formula: see text]. Let [Formula: see text] be the filtration subcategory generated by [Formula: see text]. We introduce the weak Jordan–Hölder property (WJHP) and Jordan–Hölder property (JHP) in [Formula: see text] and show that [Formula: see text] satisfies WJHP. Furthermore, [Formula: see text] satisfies JHP if and only if [Formula: see text] is proper.