A Categorical Equivalence for Stonean Residuated Lattices

We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map. We define a category wh...

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Detalles Bibliográficos
Publicado: 2019
Materias:
Boolean algebras
Stonean residuated lattices
Triples
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v107_n2_p399_Busaniche
http://hdl.handle.net/20.500.12110/paper_00393215_v107_n2_p399_Busaniche
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00393215_v107_n2_p399_Busaniche
record_format dspace
spelling paper:paper_00393215_v107_n2_p399_Busaniche2023-06-08T15:03:27Z A Categorical Equivalence for Stonean Residuated Lattices Boolean algebras Stonean residuated lattices Triples We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map. We define a category whose objects are these triples and suitably defined morphisms, and prove that we have a categorical equivalence between this category and that of Stonean residuated lattices. We compare our results with other works and show some applications of the equivalence. © 2018, Springer Science+Business Media B.V., part of Springer Nature. 2019 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v107_n2_p399_Busaniche http://hdl.handle.net/20.500.12110/paper_00393215_v107_n2_p399_Busaniche
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Boolean algebras
Stonean residuated lattices
Triples
spellingShingle Boolean algebras
Stonean residuated lattices
Triples
A Categorical Equivalence for Stonean Residuated Lattices
topic_facet Boolean algebras
Stonean residuated lattices
Triples
description We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map. We define a category whose objects are these triples and suitably defined morphisms, and prove that we have a categorical equivalence between this category and that of Stonean residuated lattices. We compare our results with other works and show some applications of the equivalence. © 2018, Springer Science+Business Media B.V., part of Springer Nature.
title A Categorical Equivalence for Stonean Residuated Lattices
title_short A Categorical Equivalence for Stonean Residuated Lattices
title_full A Categorical Equivalence for Stonean Residuated Lattices
title_fullStr A Categorical Equivalence for Stonean Residuated Lattices
title_full_unstemmed A Categorical Equivalence for Stonean Residuated Lattices
title_sort categorical equivalence for stonean residuated lattices
publishDate 2019
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v107_n2_p399_Busaniche
http://hdl.handle.net/20.500.12110/paper_00393215_v107_n2_p399_Busaniche
_version_ 1768544077454770176

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