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Abelian categories arising from cluster tilting subcategories II: quotient functors

Part of: Abelian categories

Published online by Cambridge University Press:  19 July 2019

Yu Liu  and
Panyue Zhou
Yu Liu
Affiliation:
School of Mathematics, Southwest Jiaotong University, 610031Chengdu, Sichuan, People's Republic of China (liuyu86@swjtu.edu.cn)
Panyue Zhou*
Affiliation:
College of Mathematics, Hunan Institute of Science and Technology, 414006Yueyang, Hunan, People's Republic of China (panyuezhou@163.com)
*
*Corresponding author.
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Abstract

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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.

Keywords

Extriangulated categoryabelian categorycluster tilting subcategoryquotient functor

MSC classification

Primary: 18E30: Derived categories, triangulated categories
Secondary: 18E10: Exact categories, abelian categories
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 6 , December 2020 , pp. 2721 - 2756
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Copyright
Copyright © 2019 The Royal Society of Edinburgh

References

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