Canonical extensions of lattices are more than perfect

Andrew P. K. Craig; Maria J. Gouveia; Miroslav Haviar

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arXiv · 2001.04182

Canonical extensions of lattices are more than perfect

Andrew P. K. Craig·Maria J. Gouveia·Miroslav Haviar

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Abstract

In \cite{CGH15} we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical extensions of lattices. In this continuation of \cite{CGH15} we answer Problem 2 from there by characterising the perfect lattices that are dual to TiRS frames (and hence TiRS graphs). We introduce a new subclass of perfect lattices called PTi lattices and show that the canonical extensions of lattices are PTi lattices, and so are `more' than just perfect lattices. We introduce morphisms of TiRS structures and put our correspondence between TiRS graphs and TiRS frames from \cite{CGH15} into a full categorical framework. We illustrate our correspondences between classes of perfects lattices and classes of TiRS graphs by examples.

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BibTeX RIS

Andrew P. K. Craig, Maria J. Gouveia, Miroslav Haviar. 2020-01-13. Canonical extensions of lattices are more than perfect. https://arxiv.org/abs/2001.04182

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