More on Geometric Morphisms between Realizability Toposes

Eric Faber; Jaap van Oosten

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arXiv · 1408.3984

More on Geometric Morphisms between Realizability Toposes

Eric Faber·Jaap van Oosten

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Abstract

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.

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Eric Faber, Jaap van Oosten. 2014-08-18. More on Geometric Morphisms between Realizability Toposes. https://arxiv.org/abs/1408.3984

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