Geodesic
Constructive Complete Distributivity III
Canadian mathematical bulletin, Tome 35 (1992) no. 4, pp. 537-547

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DOI

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.
DOI : 10.4153/CMB-1992-070-6
Mots-clés : 18B35, 06D10, 03G10 
Rosebrugh, Robert; Wood, R. J. Constructive Complete Distributivity III. Canadian mathematical bulletin, Tome 35 (1992) no. 4, pp. 537-547. doi: 10.4153/CMB-1992-070-6
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     title = {Constructive {Complete} {Distributivity} {III}},
     journal = {Canadian mathematical bulletin},
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     year = {1992},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-070-6/}
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