Theorems · Theorem · category theory

CategoryTheory.toSheafify_sheafifyLift_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (J : CategoryTheory.GrothendieckTopology C) {D : Type u_1}
  [inst_1 : CategoryTheory.Category.{v_1, u_1} D] [inst_2 : CategoryTheory.HasWeakSheafify J D]
  {P Q : CategoryTheory.Functor Cᵒᵖ D} (η : P ⟶ Q) (hQ : CategoryTheory.Presheaf.IsSheaf J Q)
  {Z : CategoryTheory.Functor Cᵒᵖ D} (h : Q ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.toSheafify J P)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.sheafifyLift J η hQ) h) =
    CategoryTheory.CategoryStruct.comp η h

Defined in

Mathlib.CategoryTheory.Sites.Sheafification

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify