论文标题
pre-$（n+2）$ - 角类别
Pre-$(n+2)$-angulated categories
论文作者
论文摘要
在本文中，我们介绍了前$（n+2）$类别的概念，作为Beligiannis-Reiten定义的三角形类别的更高维度类似物。我们首先表明，前$（n+2）$ - 角类别的基于掌握的完成，允许pre-$（n+2）$ - 角类别的独特结构。令$（\ Mathscr {C}，\ Mathbb {e}，\ Mathfrak {s}）$为$ n $ exangauded类别，$ \ Mathscr {x} $是$ \ mthscr {c} $的$ \ mathscr {x} $。然后，我们证明商类别$ \ MATHSCR {C}/\ MATHSCR {X} $是PRE- $（n+2）$ - 角度类别。这些结果允许构建几个pre-（n+2）$ - 角度类别的示例。此外，我们还为商$ \ mathscr {c}/\ mathscr {x} $提供了必要且充分的条件，使其成为$（n+2）$ - 角类别。
In this article, we introduce the notion of pre-$(n+2)$-angulated categories as higher dimensional analogues of pre-triangulated categories defined by Beligiannis-Reiten. We first show that the idempotent completion of a pre-$(n+2)$-angulated category admits a unique structure of pre-$(n+2)$-angulated category. Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an $n$-exangulated category and $\mathscr{X}$ be a strongly functorially finite subcategory of $\mathscr{C}$. We then show that the quotient category $\mathscr{C}/\mathscr{X}$ is a pre-$(n+2)$-angulated category.These results allow to construct several examples of pre-$(n+2)$-angulated categories. Moreover, we also give a necessary and sufficient condition for the quotient $\mathscr{C}/\mathscr{X}$ to be an $(n+2)$-angulated category.
