descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1991 English Publisher:Springer Science and Business Media LLCJournal:Applied Categorical Structures, volume 2, pages 119-144 (issn: 0927-2852, eissn: 1572-9095,

Authors: Robert Rosebrugh; R. J. Wood;

doi: 10.1007/bf00873296 , 10.1017/s0305004100070316 , 10.4153/cmb-1992-070-6

Constructive complete distributivity IV

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Abstract

AbstractA 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.

Related Organizations

Dalhousie University
Canada
Mount Allison University
Canada

Keywords

Boolean toposes, constructive complete distributivity, Topoi, Complete distributivity, constructively completely distributive lattices, subcategory of totally algebraic objects, geometric morphisms, projectives, constructive completely distributive lattices, Karoubian envelope, bicategory of relations, direct images of local homeomorphisms, Preorders, orders, domains and lattices (viewed as categories), bicategory of CCD lattices and sup-preserving arrows, left exact versions

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