We adapt the notion of generating functions for lagrangian submanifolds to
symplectic microgeometry. We show that a symplectic micromorphism always admits
a global generating function. As an application, we describe hamiltonian flows
as special symplectic micromorphisms whose local generating functions are the
solutions of Hamilton-Jacobi equations. We obtain a purely categorical
formulation of the temporal evolution in classical mechanics.Comment: 27 pages, 1 figur
