Abstract

Gabriel showed that for a unital ring R, there exists a bijective correspondence between the set of Gabriel filters of R and the set of Giraud subcategories of $\text{Mod}(R).$ In this paper we prove a result analogous to the one given by Gabriel: for a small preadditive category $\mathcal{C},$ there exists a bijective correspondence between the left Gabriel filters of $\mathcal{C}$ and Giraud subcategories of $\text{Mod}(\mathcal{C}).$

中文翻译：

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函子类别中的 Gabriel 本地化

摘要

加布里埃尔表明，对于一个单位元环- [R ，存在该组加布里埃尔滤波器之间的双射对应ř和该组吉罗子类别$\text{模组}(\mathrm{电阻}).$ 在本文中，我们证明了一个类似于 Gabriel 给出的结果：对于一个小的预加类别 $\mathcal{C},$ 的左 Gabriel 滤波器之间存在双射对应 $\mathcal{C}$ 和 Giraud 子类别 $\text{模组}(\mathcal{C}).$