  The concept of generalized functions taking values in a differentiable
manifold is extended to a functorial theory. We establish several
characterization results which allow a global intrinsic formulation both of the
theory of manifold-valued generalized functions and of generalized vector
bundle homomorphisms. As a consequence, a characterization of equivalence that
does not resort to derivatives (already known for the scalar-valued cases of
Colombeau's construction) is achieved. These results are employed to derive a
point value description of all types of generalized functions valued in
manifolds and to show that composition can be carried out unrestrictedly.
Finally, a new concept of association adapted to the present setting is
introduced.
