Let (X) over tilde -> X be a covering map and let X be a topological group. We define a category UTGCov(X) of coverings of X in which both X and (X) over tilde have universal coverings, and a category UTGGdCov (pi(l), X) of coverings of topological group-groupoid pi(l) X in which X and (G) over tilde (0) = (X) over tilde have universal coverings, and then prove the equivalence of these categories. We prove that the topological group structure of a topological group-groupoid lifts to a topological universal covering groupoid.
C1 Inonu Univ, Sci & Art Fac, Dept Math, TR-44100 Malatya, Turkey.