Geodesic
Cluster-tilting subcategories in extriangulated categories
Theory and applications of categories, Tome 34 (2019), pp. 221-242

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Let $(C,E,s)$ be an extriangulated category. We show that certain quotient categories of extriangulated categories are equivalent to module categories by some restriction of functor $E$, and in some cases, they are abelian. This result can be regarded as a simultaneous generalization of Koenig-Zhu and Demonet-Liu. In addition, we introduce the notion of maximal rigid subcategories in extriangulated categories. Cluster tilting subcategories are obviously strongly functorially finite maximal rigid subcategories, we prove that the converse is true if the 2-Calabi-Yau extriangulated categories admit a cluster tilting subcategories, which generalizes a result of Buan-Iyama-Reiten-Scott and Zhou-Zhu.

Publié le :
Classification : 18E30, 18E10
Keywords: Extriangulated categories, Cluster-tilting subcategories, Rigid subcategories, Maximal rigid subcategories, Quotient categories 
@article{TAC_2019_34_a7,
     author = {Panyue Zhou and Bin Zhu},
     title = {Cluster-tilting subcategories in extriangulated categories},
     journal = {Theory and applications of categories},
     pages = {221--242},
     publisher = {mathdoc},
     volume = {34},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a7/}
}
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Panyue Zhou; Bin Zhu. Cluster-tilting subcategories in extriangulated categories. Theory and applications of categories, Tome 34 (2019), pp. 221-242. http://geodesic.mathdoc.fr/item/TAC_2019_34_a7/