Axiomatizing subcategories of Abelian categories |
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Affiliation: | Department of Mathematics, Uppsala University, 75106 Uppsala, Sweden |
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Abstract: | We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated. |
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Keywords: | Cluster tilting Abelian category Homological algebra |
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