English

Gabriel localization in functor categories

Category Theory 2020-01-14 v1

Abstract

P. Gabriel showed that for an unital ring RR, there exists a bijective correspondence between the set of Gabriel filters of RR and the set of Giraud subcategories of Mod(R)\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 C\mathcal{C}, there exists a bijective correspondence between the Gabriel filters of C\mathcal{C} and Giraud subcategories of Mod(C)\mathrm{Mod}(\mathcal{C}).

Keywords

Cite

@article{arxiv.2001.03820,
  title  = {Gabriel localization in functor categories},
  author = {Martin Ortiz-Morales and Martha Lizbeth Shaid Sandoval-Miranda and Valente Santiago-Vargas},
  journal= {arXiv preprint arXiv:2001.03820},
  year   = {2020}
}
R2 v1 2026-06-23T13:08:46.310Z