Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the 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.
Keywords: realizability toposes, partial combinatory algebras, geometric morphisms, local operators
2010 MSC: 18B25,03D75
Theory and Applications of Categories, Vol. 29, 2014, No. 30, pp 874-895.