Duality theory for enriched Priestley spaces
Abstract
The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour that aims to extend a web of Stone-type dualities from ordered to metric structures and, more generally, to quantale-enriched categories. In particular, we improve our previous work and show how certain duality results for categories of [0,1]-enriched Priestley spaces and [0,1]-enriched relations can be restricted to functions. In a broader context, we investigate the category of quantale-enriched Priestley spaces and continuous functors, with emphasis on those properties which identify the algebraic nature of the dual of this category.
Keywords
Cite
@article{arxiv.2009.02303,
title = {Duality theory for enriched Priestley spaces},
author = {Dirk Hofmann and Pedro Nora},
journal= {arXiv preprint arXiv:2009.02303},
year = {2020}
}