Abelian categories aising from cluster tilting subcategories
Abelian categories aising from cluster tilting subcategories
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由簇倾斜子类别产生的阿贝尔类别
DOI：
10.1007/s10485-019-09590-w
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发表时间：
2020
影响因子：
0.6
通讯作者：
Panyue Zhou
中科院分区：
文献类型：
--
作者：
Yu Liu;Panyue Zhou
For a triangulated category, ifis a cluster-tilting subcategory of, then the factor categoryis an abelian category. Under certain conditions, the converse also holds. This is a very important result of cluster-tilting theory, due to Koenig–Zhu and Beligiannis. Now letbe a suitable extriangulated category, which is a simultaneous generalization of triangulated categories and exact categories. We introduce the notion of pre-cluster tilting subcategoryof, which is a generalization of cluster tilting subcategory. We show thatis cluster tilting if and only if the factor categoryis abelian. Our result generalizes the related results on a triangulated category and is new for an exact category case.
