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Geometric morphisms of realizability toposes

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Peter Johnstone

We show that every geometric morphism between realizability toposes
satisfies the condition that its inverse image commutes with the
`constant object' functors, which was assumed by John Longley in his
pioneering study of such morphisms. We also provide the answer to
something which was stated as an open problem on Jaap van Oosten's
book on realizability toposes: if a subtopos of a realizability
topos is (co)complete, it must be either the topos of sets or the
degenerate topos. And we present a new and simpler condition
equivalent to the notion of computational density for applicative
morphisms of Schonfinkel algebras.

Keywords:
realizability topos, geometric morphism, applicative morphism

2010 MSC:
Primary 18B25, secondary 03D75

*Theory and Applications of Categories,*
Vol. 28, 2013,
No. 9, pp 241-249.

Published 2013-05-03.

http://www.tac.mta.ca/tac/volumes/28/9/28-09.dvi

http://www.tac.mta.ca/tac/volumes/28/9/28-09.ps

http://www.tac.mta.ca/tac/volumes/28/9/28-09.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/9/28-09.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/28/9/28-09.ps

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