On bornological semi-abelian algebras

Detalhes bibliográficos
Autor(a) principal: Borceux, Francis
Data de Publicação: 2021
Outros Autores: Clementino, Maria Manuel
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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spelling 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
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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
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23455861
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