论文信息 - Constructive complete distributivity IV

Constructive complete distributivity IV

A complete latticeL isconstructively completely distributive, (CCD), when the sup arrow from down-closed subobjects ofL toL has a left adjoint. The Karoubian envelope of the bicategory of relations is biequivalent to the bicategory of (CCD) lattices and sup-preserving arrows. There is a restriction to order ideals and “totally algebraic” lattices. Both biequivalences have left exact versions. As applications we characterize projective sup lattices and recover a known characterization of projective frames. Also, the known characterization of nuclear sup lattices in set as completely distributive lattices is extended to yet another characterization of (CCD) lattices in a topos.

Robert D. Rosebrugh | Richard J. Wood | R. J. Wood | R. Rosebrugh

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