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

References

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