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Abelian categories arising from cluster tilting subcategories II: quotient functors

Published online by Cambridge University Press:  19 July 2019

Yu Liu
Affiliation:
School of Mathematics, Southwest Jiaotong University, 610031Chengdu, Sichuan, People's Republic of China ([email protected])
Panyue Zhou*
Affiliation:
College of Mathematics, Hunan Institute of Science and Technology, 414006Yueyang, Hunan, People's Republic of China ([email protected])
*
*Corresponding author.

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 , a functorially finite, extension closed subcategory 𝒯 of is cluster tilting if and only if ℬ /𝒯 is an abelian category.

Type
Research Article
Copyright
Copyright © 2019 The Royal Society of Edinburgh

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