论文标题
$ n $ - 扩展封闭的子类别的$ n $ escanged类别
$n$-Extension closed subcategories of $n$-exangulated categories
论文作者
论文摘要
让$ n $成为一个积极的整数。我们表明，$ n $延伸的封闭式子类别的$ n $ exangualder类别自然而然地继承了$ n $外观的结构，该结构通过限制环境$ n $ excanged结构。此外，我们表明，晦涩的公理的强大版本适用于$ n $的类别，其中$ n \ geq 2 $。这使我们能够将$ n $ exact类别描述为具有一元通货膨胀和史诗般机量的$ n $外面类别。我们还表明，对于Nakaoka和Palu引入的外侧类别条件（WIC），相当于基础添加剂类别的弱点。然后，我们应用结果表明，$ n $ n $ extact类别的$ n $扩展封闭子类别又是$ n $ - extact。此外，我们恢复并改善了Klapproth和Zhou的结果。
Let $n$ be a positive integer. We show that an $n$-extension closed subcategory of an $n$-exangulated category naturally inherits an $n$-exangulated structure through restriction of the ambient $n$-exangulated structure. Furthermore, we show that a strong version of the Obscure Axiom holds for $n$-exangulated categories, where $n \geq 2$. This allows us to characterize $n$-exact categories as $n$-exangulated categories with monic inflations and epic deflations. We also show that for an extriangulated category condition (WIC), which was introduced by Nakaoka and Palu, is equivalent to the underlying additive category being weakly idempotent complete. We then apply our results to show that $n$-extension closed subcategories of an $n$-exact category are again $n$-exact. Furthermore, we recover and improve results of Klapproth and Zhou.
