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A topos with no geometric morphism to any Boolean one

Published online by Cambridge University Press:  24 October 2008

Robert Paré
Robert Paré
Affiliation:
Dalhousie University, Halifax, N.S., Canada
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Extract

In [1], Julian Cole asked whether every topos is definable over a Boolean one. Peter Johnstone partially answered this in [2] (corollary 3·7) by giving an example of a topos admitting no bounded morphism to any Boolean topos. Here we give a simple example where boundedness is unnecessary.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 397
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Cole, J. C.. Categories of sets and models of set theory. Ph.D. thesis, University of Sussex, 1972.Google Scholar
[2]Johnstone, P. T.. Quotients of decidable objects in a topos. Math. Proc. Cambridge Philos. Soc. 93, (1983), 409–419.CrossRefGoogle Scholar