Constructive Complete Distributivity III (1992)
| Citations: | 3 - 3 self |
BibTeX
@MISC{Rosebrugh92constructivecomplete,
author = {Robert Rosebrugh and R. J. Wood and Barry W. Fawcett},
title = {Constructive Complete Distributivity III},
year = {1992}
}
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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. 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. Research partially supported by grants from NSERC Canada. Diagrams typeset using Michael Barr's diagram macros. AMS Subject Classifications: 18B35, 06D10, 03G10. Introduction A complete ordered set L is constructively completely distributive, abbreviated to (CCD)(L); if there is a left adjoint to the sup map W : DL \Gamma! L; where DL is the set of down-closed subobjects of L ordered by inclusion. The condition is equivalent to (8S ` DL) i n S j S 2 S o = n fT (S) j S 2 Sg j T 2 \PiS oj which...
Citations
| 106 | An extension of the Galois Theory of Grothendieck - Joyal, Tierney - 1984 |
| 43 | A 2-categorical approach to change of base and geometric morphisms - Carboni, Kelly, et al. - 1991 |
| 11 | Order ideals in categories - Carboni, Street - 1986 |
| 6 | Lattice Theoretic and Logical Aspects of Elementary Topoi - Mikkelsen - 1976 |
| 3 | Proarrows 1. Cahiers de Topologie et Géometrie Différentielle - Wood - 1982 |
| 2 | Constructive complete distributivity 1 - Fawcett, Wood - 1990 |
| 2 | Proarrows 2. Cahiers de topologie et g'eometrie diff'erentielle cat'egoriques - Wood - 1985 |
| 1 | Constructive complete distributivity 2 - Rosebrugh, Wood - 1991 |
