Intrinsic characterization of manifold-valued generalized functions

The concept of generalized functions taking values in a differentiable manifold ([15, 19]) 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 (as provided in [11] 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. Mathematics Subject Classification (2000): Primary: 46T30; secondary: 46F30, 53B20.