{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    AugmentedSimplexCategory.equivAugmentedCosimplicialObject.functor.comp
        CategoryTheory.CosimplicialObject.Augmented.toArrow ≅
      (CategoryTheory.Functor.mapArrowFunctor AugmentedSimplexCategory C).comp
        ((CategoryTheory.evaluation (CategoryTheory.Arrow AugmentedSimplexCategory) (CategoryTheory.Arrow C)).obj
          (CategoryTheory.Arrow.mk (CategoryTheory.WithInitial.homTo (SimplexCategory.mk 0))))