Theorems · Theorem · category theory

CategoryTheory.CategoryOfElements.costructuredArrow_yoneda_equivalence_naturality

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F₁ F₂ : CategoryTheory.Functor Cᵒᵖ (Type v)} (α : F₁ ⟶ F₂),
  (CategoryTheory.CategoryOfElements.map α).op.comp (CategoryTheory.CategoryOfElements.toCostructuredArrow F₂) =
    (CategoryTheory.CategoryOfElements.toCostructuredArrow F₁).comp (CategoryTheory.CostructuredArrow.map α)

The equivalence (-.Elements)ᵒᵖ ≅ (yoneda, -) of is actually a natural isomorphism of functors.

Defined in

Mathlib.CategoryTheory.Elements

Cited by

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Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category