Theorems · Theorem · category theory

CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence_naturality_right_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (J : CategoryTheory.GrothendieckTopology C)
  (K : CategoryTheory.GrothendieckTopology D) (G : CategoryTheory.Functor C D) {A : Type u_4}
  [inst_2 : CategoryTheory.Category.{v_4, u_4} A] [inst_3 : CategoryTheory.Functor.IsDenseSubsite J K G]
  [inst_4 : (G.sheafPushforwardContinuous A J K).IsEquivalence] [inst_5 : CategoryTheory.HasWeakSheafify J A]
  {P : CategoryTheory.Functor Dᵒᵖ A} {Q₁ Q₂ : CategoryTheory.Sheaf K A}
  (f : (CategoryTheory.Functor.IsDenseSubsite.sheafifyOfIsEquivalence J K G A).obj P ⟶ Q₁) (g : Q₁ ⟶ Q₂)
  {Z : CategoryTheory.Functor Dᵒᵖ A} (h : Q₂.obj ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence J K G)
        (CategoryTheory.CategoryStruct.comp f g))
      h =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Functor.IsDenseSubsite.sheafifyHomEquivOfIsEquivalence J K G) f)
      (CategoryTheory.CategoryStruct.comp g.hom h)

Defined in

Mathlib.CategoryTheory.Sites.DenseSubsite.Basic

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsDenseSubsiteCategoryTheory.Functor.IsEquivalenceCategoryTheory.HasWeakSheafify