  We consider orbifolds as diffeological spaces. This gives rise to a natural
notion of differentiable maps between orbifolds, making them into a subcategory
of diffeology. We prove that the diffeological approach to orbifolds is
equivalent to Satake's notion of a V-manifold and to Haefliger's notion of an
orbifold. This follows from a lemma: a diffeomorphism (in the diffeological
sense) of finite linear quotients lifts to an equivariant diffeomorphism.
