Lax orthogonal factorisation systems

Detalhes bibliográficos
Autor(a) principal: Clementino, Maria Manuel
Data de Publicação: 2016
Outros Autores: Lopez Franco, Ignacio
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/43633
https://doi.org/10.1016/j.aim.2016.07.028
Resumo: This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, Hébert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.
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spelling Lax orthogonal factorisation systemsThis paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, Hébert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.Elsevier2016-10-22info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43633http://hdl.handle.net/10316/43633https://doi.org/10.1016/j.aim.2016.07.028https://doi.org/10.1016/j.aim.2016.07.028enghttp://www.sciencedirect.com/science/article/pii/S0001870816309604Clementino, Maria ManuelLopez Franco, Ignacioinfo: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:RCAAP2021-06-29T10:02:56Zoai:estudogeral.uc.pt:10316/43633Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:26.081854Repositório 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 Lax orthogonal factorisation systems
title Lax orthogonal factorisation systems
spellingShingle Lax orthogonal factorisation systems
Clementino, Maria Manuel
title_short Lax orthogonal factorisation systems
title_full Lax orthogonal factorisation systems
title_fullStr Lax orthogonal factorisation systems
title_full_unstemmed Lax orthogonal factorisation systems
title_sort Lax orthogonal factorisation systems
author Clementino, Maria Manuel
author_facet Clementino, Maria Manuel
Lopez Franco, Ignacio
author_role author
author2 Lopez Franco, Ignacio
author2_role author
dc.contributor.author.fl_str_mv Clementino, Maria Manuel
Lopez Franco, Ignacio
description This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, Hébert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.
publishDate 2016
dc.date.none.fl_str_mv 2016-10-22
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/10316/43633
http://hdl.handle.net/10316/43633
https://doi.org/10.1016/j.aim.2016.07.028
https://doi.org/10.1016/j.aim.2016.07.028
url http://hdl.handle.net/10316/43633
https://doi.org/10.1016/j.aim.2016.07.028
dc.language.iso.fl_str_mv eng
language eng
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dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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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)
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