Quotients of exact categories by cluster tilting subcategories as module categories
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2012
- DOI:
- 10.48550/arXiv.1208.0639
- arXiv:
- arXiv:1208.0639
- Bibcode:
- 2012arXiv1208.0639D
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Category Theory
- E-Print:
- 21 pages. Slight modifications after referring. Accepted for publication in Journal of Pure and Applied Algebra