Here is a reply to Dave Yetter's query. The Magic words are "crossed modules". The basic reference is : R.Brown and C.B.Spencer, G-groupoids, crossed modules and the fundamental groupoid of a topological group, Proc.Konink. Ned. Akad. Weten. 79, 1976, 296-302. The results seem to have been known earlier. In fact if one thinks of a groupoid as being a generalisation of an equivalence relation, the proof of the equivalence of crossed modules and groups in groupoids is but a slight generalisation of the undergraduate proof that normal subgroups and congruences are equivalent ways of presenting the same information. Does this give the sort of structure theory required? Tim Porter. ++++++++++++++++++++++