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QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES

Published online by Cambridge University Press:  30 September 2019

QILIAN ZHENG
Affiliation:
Institute of Mathematics, School of Mathematics Sciences Nanjing Normal University, Nanjing 210023, P.R.China e-mails: zhengqilian1987@163.com, weijiaqun@njnu.edu.cn
JIAQUN WEI
Affiliation:
Institute of Mathematics, School of Mathematics Sciences Nanjing Normal University, Nanjing 210023, P.R.China e-mails: zhengqilian1987@163.com, weijiaqun@njnu.edu.cn

Abstract

The notion of mutation pairs of subcategories in an n-abelian category is defined in this paper. Let ${\cal D} \subseteq {\cal Z}$ be subcategories of an n-abelian category ${\cal A}$. Then the quotient category ${\cal Z}/{\cal D}$ carries naturally an (n + 2) -angulated structure whenever $ ({\cal Z},{\cal Z}) $ forms a ${\cal D} \subseteq {\cal Z}$-mutation pair and ${\cal Z}$ is extension-closed. Moreover, we introduce strongly functorially finite subcategories of n-abelian categories and show that the corresponding quotient categories are one-sided (n + 2)-angulated categories. Finally, we study homological finiteness of subcategories in a mutation pair.

Type
Research Article
Copyright
© Glasgow Mathematical Journal Trust 2019

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