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QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES

Part of: Homological algebra Abelian categories

Published online by Cambridge University Press:  30 September 2019

QILIAN ZHENG  and
JIAQUN WEI
QILIAN ZHENG
Affiliation:
Institute of Mathematics, School of Mathematics Sciences Nanjing Normal University, Nanjing 210023, P.R.China e-mails: [email protected], [email protected]
JIAQUN WEI
Affiliation:
Institute of Mathematics, School of Mathematics Sciences Nanjing Normal University, Nanjing 210023, P.R.China e-mails: [email protected], [email protected]
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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.

MSC classification

Primary: 18E10: Exact categories, abelian categories 18E30: Derived categories, triangulated categories
Secondary: 18G05: Projectives and injectives
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 3 , September 2020 , pp. 673 - 705
Copyright
© Glasgow Mathematical Journal Trust 2019

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