2020/09/04 by Dirk Hofmann, Hofmann, Dirk, Pedro Nora +1
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2009.02303
openalex publication_date 2020/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.