Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.sheafifyLift.congr_simp

∀ {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 η_1 : P ⟶ Q), η = η_1 → ∀ (hQ : CategoryTheory.Presheaf.IsSheaf J Q), J.sheafifyLift η hQ = J.sheafifyLift η_1 hQ

Defined in

Mathlib.CategoryTheory.Sites.ConcreteSheafification

Cited by

0 results in Mathlib

Foundations

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

Assumes

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