On bornological semi-abelian algebras
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/101221 https://doi.org/10.29252/cgasa.14.1.181 |
Resumo: | If T is a semi-abelian algebraic theory, we prove that the category BornT of bornological T-algebras is homological with semi-direct products. We give a formal criterion for the representability of actions in BornT and, for a bornological T-algebra X, we investigate the relation between the representability of actions on X as a T-algebra and as a bornological T- algebra. We investigate further the algebraic coherence and the algebraic local cartesian closedness of BornT and prove in particular that both properties hold in the case of bornological groups. |
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On bornological semi-abelian algebrasSemi-abelian algebraic theorybornologybornological algebrabornological groupaction representabilityalgebraic coherencelocal algebraic cartesian closednessIf T is a semi-abelian algebraic theory, we prove that the category BornT of bornological T-algebras is homological with semi-direct products. We give a formal criterion for the representability of actions in BornT and, for a bornological T-algebra X, we investigate the relation between the representability of actions on X as a T-algebra and as a bornological T- algebra. We investigate further the algebraic coherence and the algebraic local cartesian closedness of BornT and prove in particular that both properties hold in the case of bornological groups.2021info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/101221http://hdl.handle.net/10316/101221https://doi.org/10.29252/cgasa.14.1.181eng2345585323455861Borceux, FrancisClementino, Maria Manuelinfo: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:RCAAP2022-08-17T23:02:27Zoai:estudogeral.uc.pt:10316/101221Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:18:27.746328Repositório 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 |
On bornological semi-abelian algebras |
title |
On bornological semi-abelian algebras |
spellingShingle |
On bornological semi-abelian algebras Borceux, Francis Semi-abelian algebraic theory bornology bornological algebra bornological group action representability algebraic coherence local algebraic cartesian closedness |
title_short |
On bornological semi-abelian algebras |
title_full |
On bornological semi-abelian algebras |
title_fullStr |
On bornological semi-abelian algebras |
title_full_unstemmed |
On bornological semi-abelian algebras |
title_sort |
On bornological semi-abelian algebras |
author |
Borceux, Francis |
author_facet |
Borceux, Francis Clementino, Maria Manuel |
author_role |
author |
author2 |
Clementino, Maria Manuel |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Borceux, Francis Clementino, Maria Manuel |
dc.subject.por.fl_str_mv |
Semi-abelian algebraic theory bornology bornological algebra bornological group action representability algebraic coherence local algebraic cartesian closedness |
topic |
Semi-abelian algebraic theory bornology bornological algebra bornological group action representability algebraic coherence local algebraic cartesian closedness |
description |
If T is a semi-abelian algebraic theory, we prove that the category BornT of bornological T-algebras is homological with semi-direct products. We give a formal criterion for the representability of actions in BornT and, for a bornological T-algebra X, we investigate the relation between the representability of actions on X as a T-algebra and as a bornological T- algebra. We investigate further the algebraic coherence and the algebraic local cartesian closedness of BornT and prove in particular that both properties hold in the case of bornological groups. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021 |
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/10316/101221 http://hdl.handle.net/10316/101221 https://doi.org/10.29252/cgasa.14.1.181 |
url |
http://hdl.handle.net/10316/101221 https://doi.org/10.29252/cgasa.14.1.181 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
23455853 23455861 |
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 |
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 |
repository.mail.fl_str_mv |
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1799134079137873920 |