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.

中文翻译：

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n-阿贝尔范畴的商范畴

子类别中的突变对的概念n-abelian 范畴在本文中定义。让${\cal D} \subseteq {\cal Z}$是一个子类n-abelian 范畴${\cal A}$. 那么商类${\cal Z}/{\cal D}$每当$ ({\cal Z},{\cal Z}) $形成一个${\cal D} \subseteq {\cal Z}$-突变对和${\cal Z}$是扩展封闭的。此外，我们引入了强函数有限的子类别n-abelian 类别，并表明相应的商类别是单边 (n + 2) 角度类别。最后，我们研究了突变对中子类别的同调有限性。