A categorical equivalence for Stonean residuated lattices
Logic
2017-10-18 v2
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.
Keywords
Cite
@article{arxiv.1706.06332,
title = {A categorical equivalence for Stonean residuated lattices},
author = {Manuela Busaniche and Roberto Cignoli and Miguel Marcos},
journal= {arXiv preprint arXiv:1706.06332},
year = {2017}
}