  A Jet groupoid R_q over a manifold X is a special Lie groupoid consisting of
q-jets of local diffeomorphisms from X to X. As a subbundle of the q-th order
jet bundle of the trivial bundle X times X, a jet groupoid can be considered as
a nonlinear system of partial differential equations (PDE). This leads to the
concept of formal integrability. On the other hand, each jet groupoid is the
symmetry groupoid of a geometric object, modelled as a section of a natural
bundle. Using the jet groupoids, we give a local characterisation of formal
integrability for transitive jet groupoids in terms of their corresponding
geometric objects.
