ISSN:
1572-9095
Keywords:
completely distributive
;
adjunction
;
projective
;
nuclear
;
Primary
;
06D10
;
Secondary
;
18B35
;
03G10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00873296
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