{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (W : CategoryTheory.MorphismProperty C) →
          {M : Type w'} →
            [inst_2 : AddMonoid M] →
              [inst_3 : CategoryTheory.HasShift C M] →
                [inst_4 : CategoryTheory.HasShift D M] →
                  (L : CategoryTheory.Functor C D) →
                    [L.IsLocalization W] →
                      [L.CommShift M] →
                        {X Y : C} →
                          [inst_7 : CategoryTheory.Localization.HasSmallLocalizedShiftedHom W M X Y] →
                            {m : M} →
                              CategoryTheory.Localization.SmallShiftedHom W X Y m ≃
                                CategoryTheory.ShiftedHom (L.obj X) (L.obj Y) m