Theorems · Definition · category theory

PresheafOfModules.toSheafify

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R₀ : CategoryTheory.Functor Cᵒᵖ RingCat} →
        {R : CategoryTheory.Sheaf J RingCat} →
          (α : R₀ ⟶ R.obj) →
            [inst_1 : CategoryTheory.Presheaf.IsLocallyInjective J α] →
              [inst_2 : CategoryTheory.Presheaf.IsLocallySurjective J α] →
                {M₀ : PresheafOfModules R₀} →
                  {A : CategoryTheory.Sheaf J AddCommGrpCat} →
                    (φ : M₀.presheaf ⟶ A.obj) →
                      [inst_3 : CategoryTheory.Presheaf.IsLocallyInjective J φ] →
                        [inst_4 : CategoryTheory.Presheaf.IsLocallySurjective J φ] →
                          M₀ ⟶ (PresheafOfModules.restrictScalars α).obj (PresheafOfModules.sheafify α φ).val

The canonical morphism from a presheaf of modules to its associated sheaf.

Defined in

Mathlib.Algebra.Category.ModuleCat.Presheaf.Sheafify

Cited by

3 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Presheaf.IsLocallyInjectiveCategoryTheory.Presheaf.IsLocallySurjectiveCategoryTheory.Presheaf.IsLocallyInjectiveCategoryTheory.Presheaf.IsLocallySurjective