def METHOD_NAME(self):
    """
    Return the identity morphism of `Hom(S,S)`.
    EXAMPLES::
        sage: S = simplicial_complexes.Sphere(2)
        sage: H = Hom(S, S)
        sage: i = H.identity()
        sage: i.is_identity()
        True
        sage: T = SimplicialComplex([[0,1]], is_mutable=False)
        sage: G = Hom(T, T)
        sage: G.identity()
        Simplicial complex endomorphism of
         Simplicial complex with vertex set (0, 1) and facets {(0, 1)}
          Defn: 0 |--> 0
                1 |--> 1
    """
    if not self.is_endomorphism_set():
        raise TypeError("identity map is only defined for endomorphism sets")
    f = {i: i for i in self._domain.vertices()}
    return SimplicialComplexMorphism(f, self._domain, self._codomain)