QUOTIENT CATEGORIES OF n-ABELIAN CATEGORIES
AbstractThe 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.
2018 ◽
Vol 17
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pp. 1850062
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1966 ◽
Vol 9
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pp. 49-55
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2019 ◽
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pp. 383-439
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2015 ◽
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pp. 1550121
2017 ◽
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pp. 703-726
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2012 ◽
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pp. 1250149
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1971 ◽
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pp. 333-339
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2019 ◽
Vol 150
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pp. 2721-2756