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Abelian categories arising from cluster tilting subcategories II: quotient functors

  • Yu Liu (a1) and Panyue Zhou (a2)

Abstract

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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1Demonet, L. and Liu, Y.. Quotients of exact categories by cluster tilting subcategories as module categories. J. Pure Appl. Algebra 217 (2013), 2282–2297.
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3Koenig, S. and Zhu, B.. From triangulated categories to abelian categories: cluster tilting in a general framework. Math. Z. 258 (2008), 143–160.
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5Liu, Y. and Zhou, P.. Abelian categories arising from cluster tilting subcategories. arXiv: 1809.02315v1, 2018.
6Nakaoka, H. and Palu, Y.. Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories. arXiv:1605.05607.
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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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