Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.uliftYonedaEquiv_naturality

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C)
  [inst_1 : J.Subcanonical] {X Y : C} {F : CategoryTheory.Sheaf J (Type (max v v'))}
  (f : (CategoryTheory.GrothendieckTopology.uliftYoneda.{v', v, u} J).obj X ⟶ F) (g : Y ⟶ X),
  (CategoryTheory.ConcreteCategory.hom (F.obj.map g.op)) (J.uliftYonedaEquiv f) =
    J.uliftYonedaEquiv
      (CategoryTheory.CategoryStruct.comp ((CategoryTheory.GrothendieckTopology.uliftYoneda.{v', v, u} J).map g) f)

See also uliftYonedaEquiv_naturality' for a more general version.

Defined in

Mathlib.CategoryTheory.Sites.Subcanonical

Cited by

2 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GrothendieckTopology.Subcanonical