  We prove that the groupoid of transformations of rigid structures on surfaces
has a finite presentation as a 2-groupoid establishing a result first
conjectured by G.Moore and N.Seiberg. An alternative proof was given by
B.Bakalov and A.Kirillov Jr. We present some applications to TQFTs. This is
also related to recent work on the Grothendieck-Teichmuller groupoid by
P.Lochak, A.Hatcher and L.Schneps.
