Duality theory for enriched Priestley spaces

Detalhes bibliográficos
Autor(a) principal: Hofmann, Dirk
Data de Publicação: 2023
Outros Autores: Nora, Pedro
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/36589
Resumo: 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.
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spelling Duality theory for enriched Priestley spacesStone dualityMetric spacePriestley spaceQuantale-enriched categoryVarietyQuasivarietyThe 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.Elsevier2025-03-01T00:00:00Z2023-03-01T00:00:00Z2023-03info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/36589eng0022-404910.1016/j.jpaa.2022.107231Hofmann, DirkNora, Pedroinfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:10:34Zoai:ria.ua.pt:10773/36589Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:07:21.092813Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Duality theory for enriched Priestley spaces
title Duality theory for enriched Priestley spaces
spellingShingle Duality theory for enriched Priestley spaces
Hofmann, Dirk
Stone duality
Metric space
Priestley space
Quantale-enriched category
Variety
Quasivariety
title_short Duality theory for enriched Priestley spaces
title_full Duality theory for enriched Priestley spaces
title_fullStr Duality theory for enriched Priestley spaces
title_full_unstemmed Duality theory for enriched Priestley spaces
title_sort Duality theory for enriched Priestley spaces
author Hofmann, Dirk
author_facet Hofmann, Dirk
Nora, Pedro
author_role author
author2 Nora, Pedro
author2_role author
dc.contributor.author.fl_str_mv Hofmann, Dirk
Nora, Pedro
dc.subject.por.fl_str_mv Stone duality
Metric space
Priestley space
Quantale-enriched category
Variety
Quasivariety
topic Stone duality
Metric space
Priestley space
Quantale-enriched category
Variety
Quasivariety
description 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.
publishDate 2023
dc.date.none.fl_str_mv 2023-03-01T00:00:00Z
2023-03
2025-03-01T00:00:00Z
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/36589
url http://hdl.handle.net/10773/36589
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-4049
10.1016/j.jpaa.2022.107231
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
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dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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