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Theorems · Definition · category theory

SheafOfModules.Hom.val

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R : CategoryTheory.Sheaf J RingCat} → {X Y : SheafOfModules R} → X.Hom Y → (X.val ⟶ Y.val)

a morphism between the underlying presheaves of modules

Defined in
Mathlib.Algebra.Category.ModuleCat.Sheaf
Cited by
39 results in Mathlib
Foundations
Depth 39 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.pushforward · cited by 45SheafOfModules.pushforwardAlgebraicGeometry.Scheme.Modules.Hom.app · cited by 26Hom.appSheafOfModules.sectionsMap · cited by 12SheafOfModules.sectionsMapSheafOfModules.forget · cited by 10SheafOfModules.forgetSheafOfModules.hom_ext · cited by 7SheafOfModules.hom_extSheafOfModules.forgetToSheafModuleCat · cited by 2SheafOfModules.forgetToSh…SheafOfModules.restrictScalars · cited by 2SheafOfModules.restrictSc…SheafOfModules.Hom.ext · cited by 2Hom.extSheafOfModules.comp_val · cited by 1SheafOfModules.comp_valSheafOfModules.freeHomEquiv_symm_comp · cited by 1SheafOfModules.freeHomEqu…SheafOfModules.pushforward_comp_id · cited by 1SheafOfModules.pushforwar…SheafOfModules.pushforward_id_comp · cited by 1SheafOfModules.pushforwar…SheafOfModules.pushforward_map_val · cited by 1SheafOfModules.pushforwar…SheafOfModules.pushforward_assoc · cited by 1SheafOfModules.pushforwar…PresheafOfModules.toPresheaf_map_sheafificationHomEquiv_def · cited by 1PresheafOfModules.toPresh…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 · cited by 5SheafOfModules.HomHom.valCITED BYCITES

Cites13

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Cited by45

Results whose statement or proof uses this declaration.