Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.yonedaEquiv_symm_naturality_left

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C)
  [inst_1 : J.Subcanonical] {X X' : C} (f : X' ⟶ X) (F : CategoryTheory.Sheaf J (Type v))
  (x : F.obj.obj (Opposite.op X)),
  CategoryTheory.CategoryStruct.comp (J.yoneda.map f) (J.yonedaEquiv.symm x) =
    J.yonedaEquiv.symm ((CategoryTheory.ConcreteCategory.hom (F.obj.map f.op)) x)

Defined in

Mathlib.CategoryTheory.Sites.Subcanonical

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GrothendieckTopology.Subcanonical