A categorical equivalence for Stonean residuated lattices

Manuela Busaniche; Roberto Cignoli; Miguel Marcos

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arXiv · 1706.06332

A categorical equivalence for Stonean residuated lattices

Manuela Busaniche·Roberto Cignoli·Miguel Marcos

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Abstract

Distributive Stonean residuated lattices are closely related to Stone algebras since their bounded lattice reduct is a Stone algebra. In the present work we follow the ideas presented by Chen and Gr\"{a}tzer and try to apply 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.

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BibTeX RIS

Manuela Busaniche, Roberto Cignoli, Miguel Marcos. 2017-06-20. A categorical equivalence for Stonean residuated lattices. https://arxiv.org/abs/1706.06332

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