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arXiv · 1208.0639

Quotients of exact categories by cluster tilting subcategories as module categories

Laurent Demonet·Yu Liu
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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.

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Laurent Demonet, Yu Liu. 2012-08-03. Quotients of exact categories by cluster tilting subcategories as module categories. https://doi.org/10.1016/j.jpaa.2013.03.007

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