COVERING GROUPOIDS OF CATEGORICAL GROUPS

If X is a topological group, then its fundamental groupoid π1(X) is a group-groupoid which is a group object in the category of groupoids. Further if X is a path connected topological group which has a simply connected cover, then the category of covering groups of X and the category of covering groupoids of π1(X) are equivalent. In this paper we prove that if (X, x0) is an H-group, then the fundamental groupoid π1(X) is a weak categorical group. This enables one to prove that the category of the covering spaces of an H-group (X, x0) is equivalent to the category of covering groupoids of the weak categorical group π1(X).