Theorems · Theorem · category theory

CategoryTheory.toPresheafToSheafCompComposeAndSheafify_app

∀ {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 B]
  [inst_4 : CategoryTheory.HasWeakSheafify J A] (X : CategoryTheory.Functor Cᵒᵖ A),
  (CategoryTheory.toPresheafToSheafCompComposeAndSheafify J F).app X =
    (CategoryTheory.presheafToSheaf J B).map (CategoryTheory.Functor.whiskerRight (CategoryTheory.toSheafify J X) F)

Defined in

Mathlib.CategoryTheory.Sites.PreservesSheafification

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasWeakSheafify