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Cayley's Theorem states that a permutation group of a group is isomorphic to the given group. We show that this permutation group is Adams completion of the group with respect to a suitably chosen set of morphisms in the category of groups and homomorphisms.

In this note, we have obtained a Whitehead-like tower of a module by considering a suitable set of morphisms and shown that the different stages of the tower are the Adams cocompletions of the module with respect to the suitably chosen set of morphisms.