Sort u_1 →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {X : C} →
        {P : HomotopicalAlgebra.Precylinder X} →
          {Y : C} →
            {f g : X ⟶ Y} →
              P.LeftHomotopy f g →
                {C' : Type u} →
                  [inst' : CategoryTheory.Category.{v, u} C'] →
                    {X' : C'} →
                      {P' : HomotopicalAlgebra.Precylinder X'} →
                        {Y' : C'} → {f' g' : X' ⟶ Y'} → P'.LeftHomotopy f' g' → Sort u_1