Convergence and quantale-enriched categories

Detalhes bibliográficos
Autor(a) principal: Hofmann, Dirk
Data de Publicação: 2018
Outros Autores: Reis, Carla D.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/28974
Resumo: Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category.
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spelling Convergence and quantale-enriched categoriesOrdered compact Hausdorff spaceMetric spaceApproach spaceSober spaceCauchy completnessQuantale-enriched categoryGeneralising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category.Shahid Beheshti University2020-07-30T18:00:35Z2018-01-01T00:00:00Z2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/28974eng2345-5853Hofmann, DirkReis, Carla D.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:55:58Zoai:ria.ua.pt:10773/28974Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:01:23.840686Repositório 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 Convergence and quantale-enriched categories
title Convergence and quantale-enriched categories
spellingShingle Convergence and quantale-enriched categories
Hofmann, Dirk
Ordered compact Hausdorff space
Metric space
Approach space
Sober space
Cauchy completness
Quantale-enriched category
title_short Convergence and quantale-enriched categories
title_full Convergence and quantale-enriched categories
title_fullStr Convergence and quantale-enriched categories
title_full_unstemmed Convergence and quantale-enriched categories
title_sort Convergence and quantale-enriched categories
author Hofmann, Dirk
author_facet Hofmann, Dirk
Reis, Carla D.
author_role author
author2 Reis, Carla D.
author2_role author
dc.contributor.author.fl_str_mv Hofmann, Dirk
Reis, Carla D.
dc.subject.por.fl_str_mv Ordered compact Hausdorff space
Metric space
Approach space
Sober space
Cauchy completness
Quantale-enriched category
topic Ordered compact Hausdorff space
Metric space
Approach space
Sober space
Cauchy completness
Quantale-enriched category
description Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01T00:00:00Z
2018
2020-07-30T18:00:35Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/28974
url http://hdl.handle.net/10773/28974
dc.language.iso.fl_str_mv eng
language eng
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eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Shahid Beheshti University
publisher.none.fl_str_mv Shahid Beheshti University
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
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