arXiv 1706.063322017-06math.LO

Stonean剩余格的范畴等价

A categorical equivalence for Stonean residuated lattices

Manuela Busaniche, Roberto Cignoli, Miguel Marcos

摘要：

分配Stonean剩余格与Stone代数密切相关，因为它们的有界格约简是Stone代数。在目前的工作中，我们遵循陈和Grätzer提出的想法，并试图将它们应用于Stonean剩余格的情况。给定一个Stonean剩余格，我们考虑由它的布尔骨架、稠密元代数和一个连通映射构成的三元组。我们定义了一个范畴，其对象是这些三元组和适当定义的态射，并证明了我们有一个范畴之间的范畴和斯通剩余格的范畴等价。我们比较我们的结果与其他作品，并显示一些应用的等价性。

英文摘要：

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 Grätzer 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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