{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    (W : CategoryTheory.MorphismProperty C) →
      {D : Type u₂} →
        [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
          (L : CategoryTheory.Functor C D) →
            [L.IsLocalization W] →
              {X Y : C} →
                [inst_3 : CategoryTheory.Localization.HasSmallLocalizedHom W X Y] →
                  CategoryTheory.Localization.SmallHom W X Y ≃ (L.obj X ⟶ L.obj Y)