The category Gd of simplicial groupoids is shown to admit the structure of a Quillen closed model category. The usual loop group functor on the category of reduced simplicial sets and the classifying complex functor on the category of simplicial groups are extended to functors G and \(\bar W\) between the category of simplicial sets and Gd. The main result: The functors G and \(\bar W\) induce inverse homotopy equivalences of the corresponding hammock localizations.