Sciweavers

APAL
2006

Pretopologies and a uniform presentation of sup-lattices, quantales and frames

13 years 11 months ago
Pretopologies and a uniform presentation of sup-lattices, quantales and frames
We introduce the notion of infinitary preorder and use it to obtain a predicative presentation of sup-lattices by generators and relations. The method is uniform in that it extends in a modular way to obtain a presentation of quantales, as "sup-lattices on monoids", by using the notion of pretopology. Our presentation is then applied to frames, the link with Johnstone's presentation of frames is spelled out, and his theorem on freely generated frames becomes a special case of our results on quantales. The main motivation of this paper is to contribute to the development of formal topology. That is why all our definitions and proofs can be expressed within an intuitionistic and predicative foundation, like constructive type theory.
Giulia Battilotti, Giovanni Sambin
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where APAL
Authors Giulia Battilotti, Giovanni Sambin
Comments (0)