论文标题
从$ n $外面类别到$ n $ - 阿贝尔类别
From $n$-exangulated categories to $n$-abelian categories
论文作者
论文摘要
Herschend-Liu-Nakaoka引入了$ n $估算的类别的概念。它不仅是Nakaoka-palu定义的外节类别的较高维度类似物，而且还从Jasso的意义上对$ N $ extact的类别进行了同时概括（n+2）$ - 从GEISS-KELLER-OPPERMANN的意义上讲。令$ \ mathscr c $为$ n $优先类别，具有足够的投影和足够的注射器，以及$ \ Mathscr x $ a cluster倾斜子类别的$ \ Mathscr c $。在本文中，我们表明商类别$ \ mathscr c/\ mathscr x $是$ n $ -Abelian类别。这扩展了$（n+2）$ - 角类别的Zhou-Zhu的结果。此外，当它应用于$ n $ opact类别时，它突出显示了新现象。
Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a simultaneous generalization of $n$-exact categories in the sense of Jasso and $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann. Let $\mathscr C$ be an $n$-exangulated category with enough projectives and enough injectives, and $\mathscr X$ a cluster tilting subcategory of $\mathscr C$. In this article, we show that the quotient category $\mathscr C/\mathscr X$ is an $n$-abelian category. This extends a result of Zhou-Zhu for $(n+2)$-angulated categories. Moreover, it highlights new phenomena when it is applied to $n$-exact categories.
