  Michael Shub proved in 1969 that the topological conjugacy class of an
expanding endomorphism on a compact manifold is determined by its homotopy
type. In this article we generalize this result in two directions. In one
direction we consider certain expanding maps on metric spaces. In a second
direction we consider maps which are hyperbolic with respect to product cone
fields on a product manifold. A key step in the proof is to establish a
shadowing theorem for pseudo--orbits with some additional homotopy information.
