The quantale of Galois connections
Autor(a) principal: | |
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Data de Publicação: | 2005 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/7741 https://doi.org/10.1007/s00012-004-1901-1 |
Resumo: | Galois connections were originally expressed in a contravariant form with transformations that reverse (rather than preserve) order. Nowadays its covariant form (as residuated maps) is more often used since it is more convenient; namely compositions of residuated maps are handled more easily. In this paper we show that this is not a serious disadvantage of the contravariant form (at least in the natural context for uniform structures, where we need it), by introducing an operation of composition in the complete lattice Gal( L, L) of all (contravariant) Galois connections in a complete lattice L, that allows us to work with Galois connections in the same way as one usually works with residuated maps. This operation endows Gal( L, L) with a structure of quantale whenever L is a locale, allowing the description of uniform structures in terms of Galois connections. |
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7160 |
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The quantale of Galois connectionsGalois connections were originally expressed in a contravariant form with transformations that reverse (rather than preserve) order. Nowadays its covariant form (as residuated maps) is more often used since it is more convenient; namely compositions of residuated maps are handled more easily. In this paper we show that this is not a serious disadvantage of the contravariant form (at least in the natural context for uniform structures, where we need it), by introducing an operation of composition in the complete lattice Gal( L, L) of all (contravariant) Galois connections in a complete lattice L, that allows us to work with Galois connections in the same way as one usually works with residuated maps. This operation endows Gal( L, L) with a structure of quantale whenever L is a locale, allowing the description of uniform structures in terms of Galois connections.2005info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/7741http://hdl.handle.net/10316/7741https://doi.org/10.1007/s00012-004-1901-1engAlgebra Universalis. 52:4 (2005) 527-540Picado, Jorgeinfo: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:RCAAP2020-01-22T12:05:42Zoai:estudogeral.uc.pt:10316/7741Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:00:43.359157Repositório 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 |
The quantale of Galois connections |
title |
The quantale of Galois connections |
spellingShingle |
The quantale of Galois connections Picado, Jorge |
title_short |
The quantale of Galois connections |
title_full |
The quantale of Galois connections |
title_fullStr |
The quantale of Galois connections |
title_full_unstemmed |
The quantale of Galois connections |
title_sort |
The quantale of Galois connections |
author |
Picado, Jorge |
author_facet |
Picado, Jorge |
author_role |
author |
dc.contributor.author.fl_str_mv |
Picado, Jorge |
description |
Galois connections were originally expressed in a contravariant form with transformations that reverse (rather than preserve) order. Nowadays its covariant form (as residuated maps) is more often used since it is more convenient; namely compositions of residuated maps are handled more easily. In this paper we show that this is not a serious disadvantage of the contravariant form (at least in the natural context for uniform structures, where we need it), by introducing an operation of composition in the complete lattice Gal( L, L) of all (contravariant) Galois connections in a complete lattice L, that allows us to work with Galois connections in the same way as one usually works with residuated maps. This operation endows Gal( L, L) with a structure of quantale whenever L is a locale, allowing the description of uniform structures in terms of Galois connections. |
publishDate |
2005 |
dc.date.none.fl_str_mv |
2005 |
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/10316/7741 http://hdl.handle.net/10316/7741 https://doi.org/10.1007/s00012-004-1901-1 |
url |
http://hdl.handle.net/10316/7741 https://doi.org/10.1007/s00012-004-1901-1 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Algebra Universalis. 52:4 (2005) 527-540 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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 |
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RCAAP |
institution |
RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133897587425280 |