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arXiv · 2001.03820

Gabriel localization in functor categories

Martin Ortiz-Morales·Martha Lizbeth Shaid Sandoval-Miranda·Valente Santiago-Vargas
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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 $\mathrm{Mod}(\mathcal{C})$.

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Martin Ortiz-Morales, Martha Lizbeth Shaid Sandoval-Miranda, Valente Santiago-Vargas. 2020-01-12. Gabriel localization in functor categories. https://arxiv.org/abs/2001.03820

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