∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  [inst_1 :
    ∀ (n : ℕ) (f : CategoryTheory.Arrow C),
      CategoryTheory.Limits.HasWidePullback f.right (fun x => f.left) fun x => f.hom]
  {X Y : CategoryTheory.Arrow C} (F : X ⟶ Y),
  CategoryTheory.SimplicialObject.cechNerve.map F = CategoryTheory.Arrow.mapCechNerve F