  We show that \'etale correspondences between ample groupoids induce
homomorphisms of homology groups. To complement this we explore the module
categories of ample groupoids. We construct an induction-restriction adjunction
for subgroupoids, which generates a procedure for building resolutions of
arbitrary groupoid modules. These resolutions can be used to work with the Tor
picture of groupoid homology, enabling explicit descriptions of the maps in
homology induced by \'etale correspondences.
