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Constructive complete distributivity II

Published online by Cambridge University Press:  24 October 2008

Robert Rosebrugh  and
R. J. Wood
Robert Rosebrugh
Affiliation:
Department of Mathematics and Computer Science, Mount Allison University, Sackville, N.B., Canada
R. J. Wood
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, N.S., Canada
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Abstract

A complete lattice, L, is constructively completely distributive, (CCD) (L), if the sup map defined on down-closed subobjects has a left adjoint. It was known that in Boolean toposes (CCD) (L) is equivalent to (CCD) (Lop). We show here that the latter property for all L (sufficiently, for Ω.) characterizes Boolean toposes.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 245 - 249
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Fawcett, B. and Wood, R. J.. Constructive complete distributivity 1. Math. Proc. Cambridge Philos. Soc. 107 (1990), 81–89.CrossRefGoogle Scholar
[2]Johnstone, P. T.. Topos Theory (Academic Press, 1977).Google Scholar
[3]Rosebrugh, R. and Wood, R. J.. Constructive complete distributivity 3. Bull. Austral. Math. Soc. (1991), to appear.Google Scholar
[4]Street, R. and Walters, R. F. C.. Yoneda structures on 2-categories. J. Algebra 50 (1978), 350–379.CrossRefGoogle Scholar
[5]Wood, R. J.. Some remarks on total categories. J. Algebra 75 (1982), 538–545.CrossRefGoogle Scholar