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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Bibliographic Details
Published in:Studia logica 2019-04, Vol.107 (2), p.399-421
Main Authors: Busaniche, Manuela, Cignoli, Roberto, Marcos, Miguel Andrés
Format: Article
Language:English
Subjects:
Computational Linguistics
Education
Logic
Mathematical Logic and Foundations
Philosophy
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Summary: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.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-018-9800-1