{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasFiniteCoproducts C] →
        (CategoryTheory.Idempotents.toKaroubi (CategoryTheory.SimplicialObject C)).comp
            (AlgebraicTopology.DoldKan.N₂.comp AlgebraicTopology.DoldKan.Γ₂) ≅
          AlgebraicTopology.DoldKan.N₁.comp AlgebraicTopology.DoldKan.Γ₂