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Theorems · Definition · category theory

SheafOfModules.forget

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

The forgetful functor SheafOfModules.{v} R ⥤ PresheafOfModules R.val.

Defined in
Mathlib.Algebra.Category.ModuleCat.Sheaf
Cited by
10 results in Mathlib
Foundations
Depth 43 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.

SheafOfModules.evaluation · cited by 11SheafOfModules.evaluationSheafOfModules.toSheaf · cited by 6SheafOfModules.toSheafPresheafOfModules.sheafificationHomEquiv · cited by 4PresheafOfModules.sheafif…PresheafOfModules.sheafificationAdjunction · cited by 3PresheafOfModules.sheafif…PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def · cited by 1PresheafOfModules.toPresh…PresheafOfModules.toSheaf_map_sheafificationHomEquiv_symm · cited by 1PresheafOfModules.toSheaf…SheafOfModules.fullyFaithfulForget · cited by 1SheafOfModules.fullyFaith…SheafOfModules.overFunctorMap · cited by 0SheafOfModules.overFuncto…SheafOfModules.PullbackConstruction.adjunction · cited by 0PullbackConstruction.adju…PresheafOfModules.toPresheaf_map_sheafificationAdjunction_unit_app · cited by 0PresheafOfModules.toPresh…PresheafOfModules.toPresheaf_map_sheafificationHomEquiv · cited by 0PresheafOfModules.toPresh…SheafOfModules.pullbackIso · cited by 0SheafOfModules.pullbackIsoPresheafOfModules.toSheaf_map_sheafificationAdjunction_counit_app · cited by 0PresheafOfModules.toSheaf…SheafOfModules.toSheafCompSheafToPresheafIso · cited by 0SheafOfModules.toSheafCom…SheafOfModules.toSheaf_map_hom · cited by 0SheafOfModules.toSheaf_ma…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeCategoryTheory.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 473RingCatPresheafOfModules · cited by 247PresheafOfModulesSheafOfModules · cited by 188SheafOfModulesSheafOfModules.val · cited by 55SheafOfModules.valSheafOfModules.Hom.val · cited by 39Hom.valSheafOfModules.forgetCITED BYCITES

Cites13

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Cited by22

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