I'm wondering whether anyone (most likely by anyone I mean Ross Street, Andre Joyal or Ronnie Brown, but I thought I'd ask the net) knows a structure theorem for groups in GROUPOIDS. I've worked out that if G is the group of objects, H the group of connected components and A the (necessarily abelian) group of automorphisms of the identity object, then the group of arrows must by a semi-direct product of G x_H G with A, with source and target maps being projections, but I have not been able to show or find a counter-example to the conjecture that the map assigning identity maps to objects must be (\Delta, 0) and composition must be addition on the A components, and forgetting the common target/source in the other components. This seems to be something which should be known, so before putting more time in, I thought I'd ask. --David Yetter ======================================