Generating the algebraic theory of C(X): The case of partially ordered compact spaces

Detalhes bibliográficos
Autor(a) principal: Hofmann,D
Data de Publicação: 2018
Outros Autores: Nora,P, Renato Jorge Neves
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://repositorio.inesctec.pt/handle/123456789/10523
Resumo: It is known since the late 1960’s that the dual of the category of compact Hausdorff spaces and continuous maps is a variety-not ffnitary, but bounded by ?1. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is an ?1-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms on ordered compact spaces. We also characterise the ?1-copresentable partially ordered compact spaces. © Dirk Hofmann, Renato Neves, and Pedro Nora, 2018.
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spelling Generating the algebraic theory of C(X): The case of partially ordered compact spacesIt is known since the late 1960’s that the dual of the category of compact Hausdorff spaces and continuous maps is a variety-not ffnitary, but bounded by ?1. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is an ?1-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms on ordered compact spaces. We also characterise the ?1-copresentable partially ordered compact spaces. © Dirk Hofmann, Renato Neves, and Pedro Nora, 2018.2019-12-14T16:49:52Z2018-01-01T00:00:00Z2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://repositorio.inesctec.pt/handle/123456789/10523engHofmann,DNora,PRenato Jorge Nevesinfo: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:RCAAP2023-05-15T10:20:15Zoai:repositorio.inesctec.pt:123456789/10523Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:52:53.302289Repositório 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 Generating the algebraic theory of C(X): The case of partially ordered compact spaces
title Generating the algebraic theory of C(X): The case of partially ordered compact spaces
spellingShingle Generating the algebraic theory of C(X): The case of partially ordered compact spaces
Hofmann,D
title_short Generating the algebraic theory of C(X): The case of partially ordered compact spaces
title_full Generating the algebraic theory of C(X): The case of partially ordered compact spaces
title_fullStr Generating the algebraic theory of C(X): The case of partially ordered compact spaces
title_full_unstemmed Generating the algebraic theory of C(X): The case of partially ordered compact spaces
title_sort Generating the algebraic theory of C(X): The case of partially ordered compact spaces
author Hofmann,D
author_facet Hofmann,D
Nora,P
Renato Jorge Neves
author_role author
author2 Nora,P
Renato Jorge Neves
author2_role author
author
dc.contributor.author.fl_str_mv Hofmann,D
Nora,P
Renato Jorge Neves
description It is known since the late 1960’s that the dual of the category of compact Hausdorff spaces and continuous maps is a variety-not ffnitary, but bounded by ?1. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is an ?1-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms on ordered compact spaces. We also characterise the ?1-copresentable partially ordered compact spaces. © Dirk Hofmann, Renato Neves, and Pedro Nora, 2018.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01T00:00:00Z
2018
2019-12-14T16:49:52Z
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dc.identifier.uri.fl_str_mv http://repositorio.inesctec.pt/handle/123456789/10523
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dc.language.iso.fl_str_mv eng
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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