Strict monadic topology I: First separation axioms and reflections

Detalhes bibliográficos
Autor(a) principal: Janelidze, George
Data de Publicação: 2020
Outros Autores: Sobral, Manuela
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/89438
https://doi.org/10.1016/j.topol.2019.106963
Resumo: Given a monad T on the category of sets, we consider reflections of Alg(T) into its full subcategories formed by algebras satisfying natural counterparts of topological separation axioms T_0, T_1, T_2, T_ts, and T_ths; here ts stands for totally separated and ths for what we call totally homomorphically separated, which coincides with ts in the (compact Hausdorff) topological case. We ask whether these reflections satisfy simple conditions useful in categorical Galois theory, and give some partial answers in easy cases.
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spelling Strict monadic topology I: First separation axioms and reflectionsMonadic topology; Monad; Separation axiom; Galois structureGiven a monad T on the category of sets, we consider reflections of Alg(T) into its full subcategories formed by algebras satisfying natural counterparts of topological separation axioms T_0, T_1, T_2, T_ts, and T_ths; here ts stands for totally separated and ths for what we call totally homomorphically separated, which coincides with ts in the (compact Hausdorff) topological case. We ask whether these reflections satisfy simple conditions useful in categorical Galois theory, and give some partial answers in easy cases.Elsevier2020-03info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/89438http://hdl.handle.net/10316/89438https://doi.org/10.1016/j.topol.2019.106963enghttps://doi.org/10.1016/j.topol.2019.106963Janelidze, GeorgeSobral, Manuelainfo: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:RCAAP2022-05-25T01:31:35Zoai:estudogeral.uc.pt:10316/89438Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:09:45.172146Repositório 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 Strict monadic topology I: First separation axioms and reflections
title Strict monadic topology I: First separation axioms and reflections
spellingShingle Strict monadic topology I: First separation axioms and reflections
Janelidze, George
Monadic topology; Monad; Separation axiom; Galois structure
title_short Strict monadic topology I: First separation axioms and reflections
title_full Strict monadic topology I: First separation axioms and reflections
title_fullStr Strict monadic topology I: First separation axioms and reflections
title_full_unstemmed Strict monadic topology I: First separation axioms and reflections
title_sort Strict monadic topology I: First separation axioms and reflections
author Janelidze, George
author_facet Janelidze, George
Sobral, Manuela
author_role author
author2 Sobral, Manuela
author2_role author
dc.contributor.author.fl_str_mv Janelidze, George
Sobral, Manuela
dc.subject.por.fl_str_mv Monadic topology; Monad; Separation axiom; Galois structure
topic Monadic topology; Monad; Separation axiom; Galois structure
description Given a monad T on the category of sets, we consider reflections of Alg(T) into its full subcategories formed by algebras satisfying natural counterparts of topological separation axioms T_0, T_1, T_2, T_ts, and T_ths; here ts stands for totally separated and ths for what we call totally homomorphically separated, which coincides with ts in the (compact Hausdorff) topological case. We ask whether these reflections satisfy simple conditions useful in categorical Galois theory, and give some partial answers in easy cases.
publishDate 2020
dc.date.none.fl_str_mv 2020-03
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/10316/89438
http://hdl.handle.net/10316/89438
https://doi.org/10.1016/j.topol.2019.106963
url http://hdl.handle.net/10316/89438
https://doi.org/10.1016/j.topol.2019.106963
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.topol.2019.106963
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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
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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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