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Gabriel-Popescu theorem

Giraud’s subcategories and Gabriel-Popescu theorem

The Gabriel-Popescu theorem, also quoted as Popesco-Gabriel theorem (cf. the spelling in that order, which is considered wrong when in the order of the authors!) asserts that every Grothendieck category can be represented as a reflective subcategory of a category RMod{}_R Mod of modules over a unital ring, where the localization functor is exact (one calls such subcategories of module categories Giraud subcategories).

There are various generalizations, e.g.

  • Wendy Lowen, A generalization of the Gabriel-Popescu theorem, Journal of Pure and Applied Algebra 190 (1) (2004): 197–211, doi MR2043328

N. Kuhn had related results in the study of Steenrod algebra, cf. also

  • Nicholas J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra. I, American Journal of Mathematics 116 (2): 327–360 (1994) doi
  • Jacob Lurie, A theorem of Gabriel-Kuhn-Popesco, MIT math 917 notes, lecture 8

Created on April 19, 2014 at 05:06:33. See the history of this page for a list of all contributions to it.