Galois coverings of coalgebras

We introduce the concept of a Galois covering of a pointed coalgebra. Topological coverings of quivers are used to construct covering coalgebras, including a universal one for a path subcoalgebra of the path coalgebra of the Gabriel (Ext-) quiver. The theory developed shows that Galois coverings of coalgebras can be 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. Gradings in connection to coverings of quivers and representation theory were studied in the 80's by Green, Martinez-de la Pena, Bongartz, Gabriel, Riedtman, and recently for k-categories by Cibils and Marcos. Coverings of graphs are known as voltage graphs (see book Topological Graph Theory by Gross and Tucker). One 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. The paper is in J. Algebra and on the arXiv.