Theorems · Theorem · category theory

PresheafOfModules.sheafification.congr_simp

∀ {C : Type u'} [inst : CategoryTheory.Category.{v', u'} C] {J : CategoryTheory.GrothendieckTopology C}
  {R₀ : CategoryTheory.Functor Cᵒᵖ RingCat} {R : CategoryTheory.Sheaf J RingCat} (α α_1 : R₀ ⟶ R.obj) (e_α : α = α_1)
  [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],
  PresheafOfModules.sheafification α = PresheafOfModules.sheafification α_1

Defined in

Mathlib.Algebra.Category.ModuleCat.Sheaf.Localization

Cited by

0 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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