Exponential Kleisli monoids as Eilenberg-Moore algebras

Detalhes bibliográficos
Autor(a) principal: Hofmann, Dirk
Data de Publicação: 2015
Outros Autores: Mynard, Frédéric, Seal, Gavin J.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/14895
Resumo: Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.
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spelling Exponential Kleisli monoids as Eilenberg-Moore algebrasExponentiable objectMonadMonoidal categoryTopological categoryLax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.Springer Verlag2015-11-20T17:02:47Z2015-01-01T00:00:00Z2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/14895eng0927-285210.1007/s10485-013-9328-5Hofmann, DirkMynard, FrédéricSeal, Gavin J.info: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:RCAAP2024-02-22T11:27:20Zoai:ria.ua.pt:10773/14895Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:21.891387Repositório 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 Exponential Kleisli monoids as Eilenberg-Moore algebras
title Exponential Kleisli monoids as Eilenberg-Moore algebras
spellingShingle Exponential Kleisli monoids as Eilenberg-Moore algebras
Hofmann, Dirk
Exponentiable object
Monad
Monoidal category
Topological category
title_short Exponential Kleisli monoids as Eilenberg-Moore algebras
title_full Exponential Kleisli monoids as Eilenberg-Moore algebras
title_fullStr Exponential Kleisli monoids as Eilenberg-Moore algebras
title_full_unstemmed Exponential Kleisli monoids as Eilenberg-Moore algebras
title_sort Exponential Kleisli monoids as Eilenberg-Moore algebras
author Hofmann, Dirk
author_facet Hofmann, Dirk
Mynard, Frédéric
Seal, Gavin J.
author_role author
author2 Mynard, Frédéric
Seal, Gavin J.
author2_role author
author
dc.contributor.author.fl_str_mv Hofmann, Dirk
Mynard, Frédéric
Seal, Gavin J.
dc.subject.por.fl_str_mv Exponentiable object
Monad
Monoidal category
Topological category
topic Exponentiable object
Monad
Monoidal category
Topological category
description Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.
publishDate 2015
dc.date.none.fl_str_mv 2015-11-20T17:02:47Z
2015-01-01T00:00:00Z
2015
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/10773/14895
url http://hdl.handle.net/10773/14895
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0927-2852
10.1007/s10485-013-9328-5
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
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
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