∀ {J : Type u_1} {C : Type u_4} [inst : CategoryTheory.Category.{u_3, u_1} J]
  [inst_1 : CategoryTheory.Category.{u_2, u_4} C] (F : CategoryTheory.Functor J Cᵒᵖ) (X : C),
  Function.LeftInverse (fun τ => ⟨fun j => (τ.app j).unop, ⋯⟩) fun s =>
    { app := fun j => Quiver.Hom.op (↑s j), naturality := ⋯ }