{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : HomotopicalAlgebra.ModelCategory C] →
      HomotopicalAlgebra.BifibrantObject.toHoCat.comp HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject ≅
        HomotopicalAlgebra.BifibrantObject.ιCofibrantObject.comp HomotopicalAlgebra.CofibrantObject.toHoCat