  In this article, we introduce the notion of a functor on coarse spaces being
coarsely excisive- a coarse analogue of the notion of a functor on topological
spaces being excisive. Further, taking cones, a coarsely excisive functor
yields a topologically excisive functor, and for coarse topological spaces
there is an associated coarse assembly map from the topologically exicisive
functor to the coarsely excisive functor.
  We conjecture that this coarse assembly map is an isomorphism for uniformly
contractible spaces with bounded geometry, and show that the coarse isomorphism
conjecture, along with some mild technical conditions, implies that a
correspoding equivariant assembly map is injective. Particular instances of
this equivariant assembly map are the maps in the Farrell-Jones conjecture, and
in the Baum-Connes conjecture.
