论文标题
Gabriel在函子类别中的本地化
Gabriel localization in functor categories
论文作者
论文摘要
P. Gabriel表明，对于一个Unital Ring $ R $，存在$ R $的Gabriel过滤器与$ \ Mathrm {modrm {mod}（r）$的Giraud子类别之间存在的两种对应关系（请参阅第412页）。在本文中，我们证明了Gabriel的结果类似：对于一个小的preaddive类别$ \ MATHCAL {C} $，存在$ \ Mathcal {C} $的Gabriel过滤器与Giraud {C} $的Gabriel过滤器与$ \ Mathrm {modrm {mod {mod}（c} c} $的Gabriel过滤器之间的对应关系。
P. Gabriel showed that for an unital ring $R$, there exists a bijective correspondence between the set of Gabriel filters of $R$ and the set of Giraud subcategories of $\mathrm{Mod}(R)$ (see \cite[Lemme 1]{Gabriel1} on page 412). In this paper we prove analogous of Gabriel's result: for a small preadditive category $\mathcal{C}$, there exists a bijective correspondence between the Gabriel filters of $\mathcal{C}$ and Giraud subcategories of $\mathrm{Mod}(\mathcal{C})$.
