Theorems · Theorem · category theory

CategoryTheory.toSheafify_naturality

∀ {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),
  CategoryTheory.CategoryStruct.comp η (CategoryTheory.toSheafify J Q) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.toSheafify J P) (CategoryTheory.sheafifyMap J η)

Defined in

Mathlib.CategoryTheory.Sites.Sheafification

Cited by

7 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify