Categorical algebra for continuum micro physics

Using the setting of a topos equipped with a specified infinitesimal time-interval, we try in part I to clarify the idea of lawful motions as morphisms in a category whose objects are laws of motion on state spaces, and in part II to develop specific relations between states, bodies and particles. A very general scheme to make mass distributions yield notions of inertia and hence of force is discussed. Part III concerns a special notion of a body having just one point, yet containing rich microstructure; such a body is placed in space and, in general, treated like any other body. In part IV some detailed homogeneous and quadratic examples are defined.