Cayley's theorem
As stated above, the Yoneda lemma may be considered as a vast generalization of Cayley's theorem from group theory. To see this, let formula_1 be a category with a single object formula_120 such that every morphism is an isomorphism (i.e. a groupoid with one object). Then formula_121 forms a group under the operation of composition, and any group can be realized as a category in this way.