Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.yonedaEquiv_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C)
  [inst_1 : J.Subcanonical] {X : C} {F G : CategoryTheory.Sheaf J (Type v)} (α : J.yoneda.obj X ⟶ F) (β : F ⟶ G),
  J.yonedaEquiv (CategoryTheory.CategoryStruct.comp α β) =
    (CategoryTheory.ConcreteCategory.hom (β.hom.app (Opposite.op X))) (J.yonedaEquiv α)

Defined in

Mathlib.CategoryTheory.Sites.Subcanonical

Cited by

5 results in Mathlib

Foundations

Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GrothendieckTopology.Subcanonical