2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107595In an ongoing project to classify all hereditary abelian categories, we provide a classification of Ext-finite directed hereditary abelian categories satisfying Serre duality up to derived equivalence. In order to prove the classification, we will study the shapes of the Auslander-Reiten components extensively and use appropriate generalisations of tilting objects and coordinates, namely partial tilting sets and probing of objects by quasi-simples.30 pages with 12 figures; incorporated referee's commentsCategory TheoryRepresentation Theory16G20; 16G70; 18E10, 18E30text