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Serre classes for toposes

Published online by Cambridge University Press:  17 April 2009

M. Adelman  and
P.T. Johnstone
M. Adelman
Affiliation:
School of Mathematics and Physics, Macquarie University, North Ryde, New South Wales 2113, Australia
P.T. Johnstone
Affiliation:
Department of Pure Mathematics, University of Cambridge, Cambridge CB2 ISB, England.
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Abstract

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We prove first that a logical fraction functor from a topos to a topos must be a filter-power functor, then we prove that such functors can have adjoints only when the filter is principal. Finally we refine this so that we are able to prove that the filter-power of a Grothendieck topos is Grothendieck if and only if the filter is principal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1982 , pp. 103 - 115
Copyright
Copyright © Australian Mathematical Society 1982

References

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