{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    AugmentedSimplexCategory.equivAugmentedSimplicialObject.functor.comp
        CategoryTheory.SimplicialObject.Augmented.point ≅
      (CategoryTheory.evaluation AugmentedSimplexCategoryᵒᵖ C).obj (Opposite.op CategoryTheory.WithInitial.star)