Gabriel localization in functor categories
Abstract
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 $\mathrm{Mod}(\mathcal{C})$.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.03820
- arXiv:
- arXiv:2001.03820
- Bibcode:
- 2020arXiv200103820O
- Keywords:
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- Mathematics - Category Theory