We introduce the concept of a Galois covering of a pointed coalgebra. The
theory developed shows that Galois coverings of pointed coalgebras can be
concretely expressed by smash coproducts using the coaction of the automorphism
group of the covering. Thus the theory of Galois coverings is seen to be
equivalent to group gradings of coalgebras. An advantageous feature of the
coalgebra theory is that neither the grading group nor the quiver is assumed
finite in order to obtain a smash product coalgebra