Aspects of algebraic algebras

Detalhes bibliográficos
Autor(a) principal: Hofmann, Dirk
Data de Publicação: 2017
Outros Autores: Sousa, Lurdes
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/18668
Resumo: In this paper we investigate important categories lying strictly between the Kleisli category and the Eilenberg--Moore category, for a Kock-Z\"oberlein monad on an order-enriched category. Firstly, we give a characterisation of free algebras in the spirit of domain theory. Secondly, we study the existence of weighted (co)limits, both on the abstract level and for specific categories of domain theory like the category of algebraic lattices. Finally, we apply these results to give a description of the idempotent split completion of the Kleisli category of the filter monad on the category of topological spaces.
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spelling Aspects of algebraic algebrasKock-Z\"oberlein monadFilter monadContinuous latticeAlgebraic latticeWeighted (co)limitIdempotent split completionIn this paper we investigate important categories lying strictly between the Kleisli category and the Eilenberg--Moore category, for a Kock-Z\"oberlein monad on an order-enriched category. Firstly, we give a characterisation of free algebras in the spirit of domain theory. Secondly, we study the existence of weighted (co)limits, both on the abstract level and for specific categories of domain theory like the category of algebraic lattices. Finally, we apply these results to give a description of the idempotent split completion of the Kleisli category of the filter monad on the category of topological spaces.International Federation of Computational Logic2017-10-31T10:47:25Z2017-07-10T00:00:00Z2017-07-10info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/18668eng1860-597410.23638/LMCS-13(3:4)2017Hofmann, DirkSousa, Lurdesinfo: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:RCAAP2024-02-22T11:36:10Zoai:ria.ua.pt:10773/18668Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:53:36.833414Repositório 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 Aspects of algebraic algebras
title Aspects of algebraic algebras
spellingShingle Aspects of algebraic algebras
Hofmann, Dirk
Kock-Z\"oberlein monad
Filter monad
Continuous lattice
Algebraic lattice
Weighted (co)limit
Idempotent split completion
title_short Aspects of algebraic algebras
title_full Aspects of algebraic algebras
title_fullStr Aspects of algebraic algebras
title_full_unstemmed Aspects of algebraic algebras
title_sort Aspects of algebraic algebras
author Hofmann, Dirk
author_facet Hofmann, Dirk
Sousa, Lurdes
author_role author
author2 Sousa, Lurdes
author2_role author
dc.contributor.author.fl_str_mv Hofmann, Dirk
Sousa, Lurdes
dc.subject.por.fl_str_mv Kock-Z\"oberlein monad
Filter monad
Continuous lattice
Algebraic lattice
Weighted (co)limit
Idempotent split completion
topic Kock-Z\"oberlein monad
Filter monad
Continuous lattice
Algebraic lattice
Weighted (co)limit
Idempotent split completion
description In this paper we investigate important categories lying strictly between the Kleisli category and the Eilenberg--Moore category, for a Kock-Z\"oberlein monad on an order-enriched category. Firstly, we give a characterisation of free algebras in the spirit of domain theory. Secondly, we study the existence of weighted (co)limits, both on the abstract level and for specific categories of domain theory like the category of algebraic lattices. Finally, we apply these results to give a description of the idempotent split completion of the Kleisli category of the filter monad on the category of topological spaces.
publishDate 2017
dc.date.none.fl_str_mv 2017-10-31T10:47:25Z
2017-07-10T00:00:00Z
2017-07-10
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/10773/18668
url http://hdl.handle.net/10773/18668
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1860-5974
10.23638/LMCS-13(3:4)2017
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 International Federation of Computational Logic
publisher.none.fl_str_mv International Federation of Computational Logic
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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