Quotients of exact categories by cluster tilting subcategories as module categories
Quotients of exact categories by cluster tilting subcategories as module categories
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DOI：
10.1016/j.jpaa.2013.03.007
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发表时间：
2012-08
影响因子：
0.8
通讯作者：
Laurent Demonet;Y. Liu
中科院分区：
文献类型：
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作者：
Laurent Demonet;Y. Liu
证明了正合范畴的某些子商范畴是交换的。这推广了Koenig-Zhu在（代数）三角范畴中的一个结果。作为一个特例，如果具有足够投射和内射的正合范畴B有一个簇倾斜子范畴M，则B/M是阿贝尔范畴.更确切地说，它等价于M <$上的可表示模范畴。
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 M¯.