  Geometric morphisms between realizability toposes are studied in terms of
morphisms between partial combinatory algebras (pcas). The morphisms inducing
geometric morphisms (the {\em computationally dense\/} ones) are seen to be the
ones whose `lifts' to a kind of completion have right adjoints. We characterize
topos inclusions corresponding to a general form of relative computability. We
characterize pcas whose realizability topos admits a geometric morphism to the
effective topos.
