[Merged by Bors] - feat(CategoryTheory/Sites): categories of sheaves are Grothendieck abelian - #19986
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[Merged by Bors] - feat(CategoryTheory/Sites): categories of sheaves are Grothendieck abelian#19986joelriou wants to merge 59 commits into
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…19979) In this file, we show that if `J : GrothendieckTopology C` and `A` is a preadditive category which has a separator (and suitable coproducts), then `Sheaf J A` has a separator. General results about generators are moved to a directory `CategoryTheory.Generator`. Together with #19914, we shall be able to deduce that categories of abelian sheaves are Grothendieck abelian categories (cf. #19986).
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Thanks!
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🚀 Pull request has been placed on the maintainer queue by dagurtomas. |
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Co-authored-by: Dagur Asgeirsson <dagurtomas@gmail.com>
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Thanks very much @dagurtomas for the reviews! |
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…elian (#19986) If `J` is a Grothendieck topology on a small category `C : Type v`, and `A : Type u₁` (with `Category.{v} A`) is a Grothendieck abelian category, then `Sheaf J A` is a Grothendieck abelian category. Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com> Co-authored-by: Paul Reichert <preichert@noreply.codeberg.org>
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…elian (#19986) If `J` is a Grothendieck topology on a small category `C : Type v`, and `A : Type u₁` (with `Category.{v} A`) is a Grothendieck abelian category, then `Sheaf J A` is a Grothendieck abelian category. Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com> Co-authored-by: Paul Reichert <preichert@noreply.codeberg.org>
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Pull request successfully merged into master. Build succeeded! And happy new year! 🎉 |
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If
Jis a Grothendieck topology on a small categoryC : Type v, andA : Type u₁(withCategory.{v} A) is a Grothendieck abelian category, thenSheaf J Ais a Grothendieck abelian category.