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Abelian categories arising from cluster tilting subcategories II: quotient functors

  • Yu Liu (a1) and Panyue Zhou (a2)


In this paper, we consider a kind of ideal quotient of an extriangulated category such that the ideal is the kernel of a functor from this extriangulated category to an abelian category. We study a condition when the functor is dense and full, in another word, the ideal quotient becomes abelian. Moreover, a new equivalent characterization of cluster tilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2-Calabi-Yau triangulated category ℬ, a functorially finite, extension closed subcategory 𝒯 of ℬ is cluster tilting if and only if ℬ /𝒯 is an abelian category.


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8Zhou, P. and Zhu, B.. Cluster-tilting subcategories in extriangulated categories. Theory Appl. Categ. 34 (2019), 221–242.


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