Mathlib Map

Theorems · Definition · category theory

SheafOfModules.toSheaf

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      (R : CategoryTheory.Sheaf J RingCat) →
        CategoryTheory.Functor (SheafOfModules R) (CategoryTheory.Sheaf J AddCommGrpCat)

The forget functor SheafOfModules R ⥤ Sheaf J AddCommGrpCat.

Defined in
Mathlib.Algebra.Category.ModuleCat.Sheaf
Cited by
6 results in Mathlib
Foundations
Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm · cited by 1PresheafOfModules.toSheaf…PresheafOfModules.sheafificationCompToSheaf · cited by 1PresheafOfModules.sheafif…PresheafOfModules.toPresheaf_map_sheafificationHomEquiv · cited by 0PresheafOfModules.toPresh…PresheafOfModules.inverseImage_W_toPresheaf_eq_inverseImage_isomorphisms · cited by 0PresheafOfModules.inverse…PresheafOfModules.toSheaf_map_sheafificationAdjunction_counit_app · cited by 0PresheafOfModules.toSheaf…SheafOfModules.toSheafCompSheafToPresheafIso · cited by 0SheafOfModules.toSheafCom…SheafOfModules.toSheaf_map_hom · cited by 0SheafOfModules.toSheaf_ma…SheafOfModules.toSheaf_obj_obj · cited by 0SheafOfModules.toSheaf_ob…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objCategoryTheory.Presheaf.IsSheaf · cited by 991Presheaf.IsSheafCategoryTheory.Sheaf · cited by 763CategoryTheory.SheafRingCat · cited by 473RingCatAddCommGrpCat · cited by 462AddCommGrpCatSheafOfModules · cited by 188SheafOfModulesPresheafOfModules.presheaf · cited by 85PresheafOfModules.presheafSheafOfModules.val · cited by 55SheafOfModules.valSheafOfModules.toSheafCITED BYCITES

Cites18

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Cited by8

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