论文标题
$ n $外观类别的愿望完成
Idempotent completions of $n$-exangulated categories
论文作者
论文摘要
假设$（\ Mathcal {C}，\ Mathbb {e}，\ Mathfrak {s}）$是$ n $ exangauded类别。我们表明，$ \ mathcal {c} $的diDempotent完成和弱掌完成的类别。此外，我们还表明，$ \ Mathcal {c} $的规范包含函数在其（分别弱）idempotent完成中为$ n $ exexangualder，$ n $ n $ exangalualder fuctors中的$ n $ exemantal in $（\ mathcal {c}，\ mathbb foff），\ mathbb {e e}，\ math。 IDEMPOTENT完整的$ N $外面类别。此外，我们证明，如果$（\ Mathcal {c}，\ Mathbb {e}，\ Mathfrak {s}）$是$ n $ - extact，那么它的（resp。feal）diadempotent的完成也是如此。我们注意到，我们的举证方法与外侧和$（n+2）$ - 角度案例有很大不同。但是，我们的构造在既定案例中恢复已知的结构，最高$ n $ n $ exymormatirist的类别。
Suppose $(\mathcal{C},\mathbb{E},\mathfrak{s})$ is an $n$-exangulated category. We show that the idempotent completion and the weak idempotent completion of $\mathcal{C}$ are again $n$-exangulated categories. Furthermore, we also show that the canonical inclusion functor of $\mathcal{C}$ into its (resp. weak) idempotent completion is $n$-exangulated and $2$-universal among $n$-exangulated functors from $(\mathcal{C},\mathbb{E},\mathfrak{s})$ to (resp. weakly) idempotent complete $n$-exangulated categories. Furthermore, we prove that if $(\mathcal{C},\mathbb{E},\mathfrak{s})$ is $n$-exact, then so too is its (resp. weak) idempotent completion. We note that our methods of proof differ substantially from the extriangulated and $(n+2)$-angulated cases. However, our constructions recover the known structures in the established cases up to $n$-exangulated isomorphism of $n$-exangulated categories.
