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Constructive Complete Distributivity III

Published online by Cambridge University Press:  20 November 2018

Robert Rosebrugh  and
R. J. Wood
Robert Rosebrugh
Affiliation:
Department of Mathematics and Computer Science Mount Allison University Sackville, New Brunswick
R. J. Wood
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie University Halifax, Nova Scotia
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Abstract

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A complete lattice L is constructively completely distributive,(CCD)(L), if the sup map defined on down closed subobjects has a left adjoint. We characterize preservation of this property by left exact functors between toposes using a "logical comparison transformation". The characterization is applied to (direct images of) geometric morphisms to show that local homeomorphisms (in particular, product functors) preserve (CCD) objects, while preserving (CCD) objects implies openness.

Keywords

18B3506D1003G10

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 537 - 547
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Carboni, Aurelio, Kelly, G. M. and Wood, R. J., A 2-categorical approach to change of base and geometric morphisms 1, Cahiers de topologie et géométrie différentielle catégoriques XXXII(1991), 47–95.Google Scholar
2. Carboni, Aurelio and Street, Ross, Order ideals in categories, Pacific Journal of Mathematics (2) 124(1986), 275–278.Google Scholar
3. Fawcett, Barry and Wood, R. J., Constructive complete distributivity 1, Math. Proc. Cam. Phil. Soc. 107(1990), 81–89.Google Scholar
4. Joyal, André and Tierney, Myles, An Extension of the Galois Theory of Grothendieck, Memoirs of the American Mathematical Society 309, American Mathematical Society, 1984.Google Scholar
5. Mikkelsen, C. J., Lattice theoretic and logical aspects of elementary topoi, Publications Series 25, Aarhus Universitet, 1976.Google Scholar
6. Rosebrugh, Robert and Wood, R. J., Constructive complete distributive 2, Math. Proc. Camb. Phil. Soc. 110(1991), 245–249.Google Scholar
7. Wood, R. J., Proarrows 1, Cahiers de topologie et géométrie différentielle catégoriques XXIII(1982), 279–290.Google Scholar
8. Wood, R. J., Proarrows 2, Cahiers de topologie et géométrie différentielle catégoriques XXVI(1985), 135— 168.Google Scholar