论文标题
两个新类别类别的新类
Two new classes of n-exangulated categories
论文作者
论文摘要
Herschend-Liu-Nakaoka引入了$ n $估算的类别的概念。它不仅是Nakaoka-palu定义的外节类别的较高维度类似物，而且还提供了$ n $ - excACT类别和$（n+2）$ angulated类别的同时概括。令$ \ mathcal c $为$ n $外面类别，$ \ Mathcal x $ a $ \ mathcal c $的完整子类别。如果$ \ MATHCAL X $满足$ \ MATHCAL X \ subseteq \ Mathcal P \ Cap \ Mathcal I $，那么我们为理想的$ \ Mathcal C/\ Mathcal x $提供了必要和足够的条件，将其作为$ n $ excal的类别，其中$ \ Mathcal p $（其中$ \ Mathcal p $）upplotive comptistive comptistive。 Injective）$ \ Mathcal C $中的对象。此外，我们在$ \ Mathcal c $中定义了$ n $ proper类的概念。如果$ξ$是$ \ Mathcal C $中的$ n $ proper类，那么我们证明$ \ Mathcal c $允许一个新的$ n $ exanged结构。这两种方式给出了$ n $的类别，这些类别既不是$ n $ extact也不是$（n+2）$ - 一般而言。
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 and $(n+2)$-angulated categories. Let $\mathcal C$ be an $n$-exangulated category and $\mathcal X$ a full subcategory of $\mathcal C$. If $\mathcal X$ satisfies $\mathcal X\subseteq\mathcal P\cap\mathcal I$, then we give a necessary and sufficient condition for the ideal quotient $\mathcal C/\mathcal X$ to be an $n$-exangulated category, where $\mathcal P$ (resp. $\mathcal I$) is the full subcategory of projective (resp. injective) objects in $\mathcal C$. In addition, we define the notion of $n$-proper class in $\mathcal C$. If $ξ$ is an $n$-proper class in $\mathcal C$, then we prove that $\mathcal C$ admits a new $n$-exangulated structure. These two ways give $n$-exangulated categories which are neither $n$-exact nor $(n+2)$-angulated in general.
