∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {F : CategoryTheory.Functor Cᵒᵖ (Type v)} {Y : C}
  (homEquiv homEquiv_1 : {X : C} → (X ⟶ Y) ≃ F.obj (Opposite.op X)) (e_homEquiv : homEquiv = homEquiv_1)
  (homEquiv_comp :
    ∀ {X X' : C} (f : X ⟶ X') (g : X' ⟶ Y),
      homEquiv (CategoryTheory.CategoryStruct.comp f g) = F.map f.op (homEquiv g)),
  { homEquiv := homEquiv, homEquiv_comp := homEquiv_comp } = { homEquiv := homEquiv_1, homEquiv_comp := ⋯ }