Classification of abelian hereditary directed categories satisfying serre duality

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8 Citations (Scopus)


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 Auslander- Reiten components extensively and use appropriate generalizations of tilting objects and coordinates, namely partial tilting sets and probing of objects by quasi-simples.

Original languageEnglish
Pages (from-to)2467-2503
Number of pages37
JournalTransactions of the American Mathematical Society
Issue number5
Publication statusPublished - May 2008
Externally publishedYes


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