∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.IsIdempotentComplete C] [inst_3 : CategoryTheory.Limits.HasFiniteCoproducts C]
  (X : CategoryTheory.SimplicialObject C),
  (CategoryTheory.Idempotents.DoldKan.isoN₁.hom.app X).f = AlgebraicTopology.DoldKan.PInfty