∀ (C : Type u_2) [inst : CategoryTheory.Category.{u_1, u_2} C] [inst_1 : CategoryTheory.Preadditive C]
  {X Y Z : CategoryTheory.CosimplicialObject C} (f : X ⟶ Y) (g : Y ⟶ Z),
  AlgebraicTopology.AlternatingCofaceMapComplex.map (CategoryTheory.CategoryStruct.comp f g) =
    CategoryTheory.CategoryStruct.comp (AlgebraicTopology.AlternatingCofaceMapComplex.map f)
      (AlgebraicTopology.AlternatingCofaceMapComplex.map g)