Theorems · Theorem · category theory

CategoryTheory.sheafifyLift_comp

∀ {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]
  {F P Q : CategoryTheory.Functor Cᵒᵖ D} (a : F ⟶ P) (hP : CategoryTheory.Presheaf.IsSheaf J P) (η : P ⟶ Q)
  (hQ : CategoryTheory.Presheaf.IsSheaf J Q),
  CategoryTheory.sheafifyLift J (CategoryTheory.CategoryStruct.comp a η) hQ =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.sheafifyLift J a hP) η

Defined in

Mathlib.CategoryTheory.Sites.Sheafification

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify