∀ (C : Type u_1) [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : HomotopicalAlgebra.ModelCategory C],
  (HomotopicalAlgebra.CofibrantObject.HoCat.localizerMorphismResolution C).functor =
    HomotopicalAlgebra.CofibrantObject.HoCat.resolution