Classification of abelian hereditary directed categories satisfying Serre duality

Details Classification of abelian hereditary directed categories satisfying Serre duality Classification of abelian hereditary directed categories satisfying Serre duality

2006-01-17

arxiv.org/abs/math/0601418v3

Mathematics

Category Theory

30 pages with 12 figures; incorporated referee's comments

Scientific paper

In 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.

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