∀ (X : SimplexCategory),
  { left := SSet.stdSimplex.map (CategoryTheory.CategoryStruct.id X),
      right :=
        CategoryTheory.Limits.terminal.from
          { left := SSet.stdSimplex.obj X, right := ⊤_ Type u_1,
              hom :=
                {
                  app := fun x =>
                    CategoryTheory.Limits.terminal.from
                      (((CategoryTheory.Functor.id (CategoryTheory.SimplicialObject (Type u_1))).obj
                            (SSet.stdSimplex.obj X)).obj
                        x),
                  naturality := ⋯ } }.right,
      w := ⋯ } =
    CategoryTheory.CategoryStruct.id
      { left := SSet.stdSimplex.obj X, right := ⊤_ Type u_1,
        hom :=
          {
            app := fun x =>
              CategoryTheory.Limits.terminal.from
                (((CategoryTheory.Functor.id (CategoryTheory.SimplicialObject (Type u_1))).obj
                      (SSet.stdSimplex.obj X)).obj
                  x),
            naturality := ⋯ } }