Duality theory for enriched Priestley spaces
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | |
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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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 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
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 |
eu_rights_str_mv |
embargoedAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799137728722370560 |