More on geometric morphisms between realizability toposes

Eric Faber and Jaap van Oosten

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.

Published 2014-12-19.

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