On biadjoint triangles
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/43827 |
Resumo: | We prove a biadjoint triangle theorem and its strict version, which are 2-dimensional analogues of the adjoint triangle theorem of Dubuc. Similarly to the 1-dimensional case, we demonstrate how we can apply our results to get the pseudomonadicity characterization (due to Le Creurer, Marmolejo and Vitale). Furthermore, we study applications of our main theorems in the context of the 2-monadic approach to coherence. As a direct consequence of our strict biadjoint triangle theorem, we give the construction (due to Lack) of the left 2-adjoint to the inclusion of the strict algebras into the pseudoalgebras. In the last section, we give two brief applications on lifting biadjunctions and pseudo-Kan extensions. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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On biadjoint trianglesWe prove a biadjoint triangle theorem and its strict version, which are 2-dimensional analogues of the adjoint triangle theorem of Dubuc. Similarly to the 1-dimensional case, we demonstrate how we can apply our results to get the pseudomonadicity characterization (due to Le Creurer, Marmolejo and Vitale). Furthermore, we study applications of our main theorems in the context of the 2-monadic approach to coherence. As a direct consequence of our strict biadjoint triangle theorem, we give the construction (due to Lack) of the left 2-adjoint to the inclusion of the strict algebras into the pseudoalgebras. In the last section, we give two brief applications on lifting biadjunctions and pseudo-Kan extensions.Mount Allison University2016info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43827http://hdl.handle.net/10316/43827enghttps://www.emis.de/journals/TAC/volumes/31/9/31-09abs.htmlLucatelli Nunes, Fernandoinfo: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:RCAAP2020-05-25T12:13:09Zoai:estudogeral.uc.pt:10316/43827Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:28.614199Repositório 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 biadjoint triangles |
title |
On biadjoint triangles |
spellingShingle |
On biadjoint triangles Lucatelli Nunes, Fernando |
title_short |
On biadjoint triangles |
title_full |
On biadjoint triangles |
title_fullStr |
On biadjoint triangles |
title_full_unstemmed |
On biadjoint triangles |
title_sort |
On biadjoint triangles |
author |
Lucatelli Nunes, Fernando |
author_facet |
Lucatelli Nunes, Fernando |
author_role |
author |
dc.contributor.author.fl_str_mv |
Lucatelli Nunes, Fernando |
description |
We prove a biadjoint triangle theorem and its strict version, which are 2-dimensional analogues of the adjoint triangle theorem of Dubuc. Similarly to the 1-dimensional case, we demonstrate how we can apply our results to get the pseudomonadicity characterization (due to Le Creurer, Marmolejo and Vitale). Furthermore, we study applications of our main theorems in the context of the 2-monadic approach to coherence. As a direct consequence of our strict biadjoint triangle theorem, we give the construction (due to Lack) of the left 2-adjoint to the inclusion of the strict algebras into the pseudoalgebras. In the last section, we give two brief applications on lifting biadjunctions and pseudo-Kan extensions. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016 |
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/10316/43827 http://hdl.handle.net/10316/43827 |
url |
http://hdl.handle.net/10316/43827 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://www.emis.de/journals/TAC/volumes/31/9/31-09abs.html |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Mount Allison University |
publisher.none.fl_str_mv |
Mount Allison University |
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 |
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RCAAP |
reponame_str |
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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1799133821580345345 |