Quotients of exact categories by cluster tilting subcategories as module categories
arXiv:1208.0639 · doi:10.1016/j.jpaa.2013.03.007
Abstract
We prove that some subquotient categories of exact categories are abelian. This generalizes a result by Koenig-Zhu in the case of (algebraic) triangulated categories. As a particular case, if an exact category B with enough projectives and injectives has a cluster tilting subcategory M, then B/M is abelian. More precisely, it is equivalent to the category of finitely presented modules over the stable category of M.
21 pages. Slight modifications after referring. Accepted for publication in Journal of Pure and Applied Algebra
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Cited by in corpus (11)
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- Abelian categories arising from cluster-tilting subcategories II: quotient functors
- Hearts of twin Cotorsion pairs on extriangulated categories
- Localizations of the hearts of cotorsion pairs associated with mutations
- Abelian quotients of the categories of short exact sequences
- Hearts of twin cotorsion pairs on exact categories
- Gorenstein dimension of abelian categories
- Hearts of cotorsion pairs are functor categories over cohearts
- Largest exact structures and almost split sequences on hearts of twin cotorsion pairs
- Abelian quotients arising from extriangulated categories via morphism categories
- From -exangulated categories to -abelian categories