Theorems · Theorem · category theory

CategoryTheory.sheafComposeIso_hom_fac_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {A : Type u_1}
  {B : Type u_2} [inst_1 : CategoryTheory.Category.{v_1, u_1} A] [inst_2 : CategoryTheory.Category.{v_2, u_2} B]
  (F : CategoryTheory.Functor A B) [inst_3 : CategoryTheory.HasWeakSheafify J A]
  [inst_4 : CategoryTheory.HasWeakSheafify J B] [inst_5 : J.HasSheafCompose F] [inst_6 : J.PreservesSheafification F]
  (P : CategoryTheory.Functor Cᵒᵖ A) {Z : CategoryTheory.Functor Cᵒᵖ B} (h : (CategoryTheory.sheafify J P).comp F ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.toSheafify J (P.comp F))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.sheafifyComposeIso J F P).hom h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.whiskerRight (CategoryTheory.toSheafify J P) F) h

Defined in

Mathlib.CategoryTheory.Sites.PreservesSheafification

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.HasSheafComposeCategoryTheory.GrothendieckTopology.PreservesSheafification