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

Detalhes bibliográficos
Autor(a) principal: Hofmann, Dirk
Data de Publicação: 2018
Outros Autores: Neves, Renato, 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/10773/28976
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 finitary, but bounded by $\aleph_1$. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is a $\aleph_1$-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms. We also characterise the $\aleph_1$-copresentable partially ordered compact spaces.
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spelling Generating the algebraic theory of C(X): the case of partially ordered compact spacesOrdered compact spaceQuasivarietyDualityCoalgebraVietoris functorCopresentable objectMetrisableIt is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety -- not finitary, but bounded by $\aleph_1$. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is a $\aleph_1$-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms. We also characterise the $\aleph_1$-copresentable partially ordered compact spaces.2020-07-30T18:21:42Z2018-01-01T00:00:00Z2018info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/28976eng1201-561XHofmann, DirkNeves, RenatoNora, Pedroinfo: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:10773/28976Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:01:23.931641Repositório 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, Dirk
Ordered compact space
Quasivariety
Duality
Coalgebra
Vietoris functor
Copresentable object
Metrisable
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, Dirk
author_facet Hofmann, Dirk
Neves, Renato
Nora, Pedro
author_role author
author2 Neves, Renato
Nora, Pedro
author2_role author
author
dc.contributor.author.fl_str_mv Hofmann, Dirk
Neves, Renato
Nora, Pedro
dc.subject.por.fl_str_mv Ordered compact space
Quasivariety
Duality
Coalgebra
Vietoris functor
Copresentable object
Metrisable
topic Ordered compact space
Quasivariety
Duality
Coalgebra
Vietoris functor
Copresentable object
Metrisable
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 finitary, but bounded by $\aleph_1$. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is a $\aleph_1$-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms. We also characterise the $\aleph_1$-copresentable partially ordered compact spaces.
publishDate 2018
dc.date.none.fl_str_mv 2018-01-01T00:00:00Z
2018
2020-07-30T18:21:42Z
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/10773/28976
url http://hdl.handle.net/10773/28976
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1201-561X
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron:RCAAP
instname_str 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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