Studia Logica

, Volume 107, Issue 2, pp 399–421 | Cite as

A Categorical Equivalence for Stonean Residuated Lattices

  • Manuela BusanicheEmail author
  • Roberto Cignoli
  • Miguel Andrés Marcos


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.


Stonean residuated lattices Boolean algebras Triples 


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Authors and Affiliations

  1. 1.Instituto de Matemática Aplicada del Litoral, UNL, CONICET, FIQPredio Dr. Alberto Cassano del CCT-CONICET-Santa FeSanta FeArgentina
  2. 2.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina

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