On biadjoint triangles

Detalhes bibliográficos
Autor(a) principal: Lucatelli Nunes, Fernando
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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spelling 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
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dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10316/43827
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dc.publisher.none.fl_str_mv Mount Allison University
publisher.none.fl_str_mv Mount Allison University
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