Theorems · Theorem · category theory

PresheafOfModules.inverseImage_W_toPresheaf_eq_inverseImage_isomorphisms

∀ {C : Type u'} [inst : CategoryTheory.Category.{v', u'} 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]
  [inst_3 : J.WEqualsLocallyBijective AddCommGrpCat] [inst_4 : CategoryTheory.HasWeakSheafify J AddCommGrpCat],
  J.W.inverseImage (PresheafOfModules.toPresheaf R₀) =
    (CategoryTheory.MorphismProperty.isomorphisms (SheafOfModules R)).inverseImage (PresheafOfModules.sheafification α)

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Localization

Cited by

0 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Presheaf.IsLocallyInjectiveCategoryTheory.Presheaf.IsLocallySurjectiveCategoryTheory.GrothendieckTopology.WEqualsLocallyBijectiveCategoryTheory.HasWeakSheafify