More on Geometric Morphisms between Realizability Toposes
Eric Faber, Jaap van Oosten · Theory and applications of categories · 2014
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.