Constructive complete distributivity IV
| ISSN: |
1572-9095
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| Keywords: |
completely distributive ; adjunction ; projective ; nuclear ; Primary ; 06D10 ; Secondary ; 18B35 ; 03G10
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| Source: |
Springer Online Journal Archives 1860-2000
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| Topics: |
Mathematics
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| 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.
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| Type of Medium: |
Electronic Resource
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| URL: |