Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type w}
  [inst_1 : CategoryTheory.Category.{w', w} D]
  [inst_2 :
    ∀ (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) (S : J.Cover X), CategoryTheory.Limits.HasMultiequalizer (S.index P)]
  [inst_3 : ∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ D] {P Q : CategoryTheory.Functor Cᵒᵖ D}
  (η : P ⟶ Q) (hQ : CategoryTheory.Presheaf.IsSheaf J Q),
  CategoryTheory.CategoryStruct.comp (J.toSheafify P) (J.sheafifyLift η hQ) = η

Defined in

Mathlib.CategoryTheory.Sites.ConcreteSheafification

Cited by

3 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasMultiequalizerCategoryTheory.Limits.HasColimitsOfShape