∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {X : CategoryTheory.SimplicialObject C} (q n : ℕ),
  CategoryTheory.CategoryStruct.comp ((AlgebraicTopology.DoldKan.P q).f n) ((AlgebraicTopology.DoldKan.P q).f n) =
    (AlgebraicTopology.DoldKan.P q).f n