1. Axiomatizing subcategories of Abelian categories
- Author
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Sondre Kvamme
- Subjects
Subcategory ,Pure mathematics ,Algebra and Number Theory ,Homological algebra ,Cluster tilting ,Mathematics - Category Theory ,Algebra and Logic ,Abelian category ,Mathematics::K-Theory and Homology ,Mathematics::Category Theory ,FOS: Mathematics ,Category Theory (math.CT) ,Representation Theory (math.RT) ,Abelian group ,Mathematics::Representation Theory ,Mathematics - Representation Theory ,Axiom ,Algebra och logik ,Mathematics - Abstract
We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find intrinsic 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., Comment: 29 pages. Accepted for publication in Journal of Pure and Applied Algebra
- Published
- 2022
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