Theorems · Theorem · category theory

CategoryTheory.sheafifyMap_sheafifyLift

∀ {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 R : CategoryTheory.Functor Cᵒᵖ D} (η : P ⟶ Q) (γ : Q ⟶ R) (hR : CategoryTheory.Presheaf.IsSheaf J R),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.sheafifyMap J η) (CategoryTheory.sheafifyLift J γ hR) =
    CategoryTheory.sheafifyLift J (CategoryTheory.CategoryStruct.comp η γ) hR

Defined in

Mathlib.CategoryTheory.Sites.Sheafification

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify