The term Stone-type duality often refers to a dual equivalence between category of lattices or other partially ordered structures on one side and topological the other. This paper is part larger endeavour that aims extend web dualities from metric and, more generally, quantale-enriched categories. In particular, we improve our previous work show how certain results for categories [ 0 , 1 ] -enr...

We present a new Priestley-style topological duality for bounded N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that for our topological ...

Traditionally in natural duality theory the algebras carry no topology and the objects on the dual side are structured Boolean spaces. Given a duality, one may ask when the topology can be swapped to the other side to yield a partner duality (or, better, a dual equivalence) between a category of topological algebras and a category of structures. A prototype for this procedure is provided by the...

The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality...

A piggyback duality and a translation process between this one and a Priestley duality for each subvariety of involutive Stone algebras and regular o-De Morgan algebras is presented. As a consequence we describe free algebras and the prime spectrum of each subvariety.

Recently, several authors extended Priestley duality for distributive lattices [9] to other classes of algebras, such as, e.g. distributive lattices with operators [7], MV -algebras [8], MTL and IMTL algebras [2]. In [5] necessary and sufficient conditions for a normally presented variety to be naturally dualizable, in the sense of [6], i.e. with respect to a discrete topology, have been provid...

In this work we develop a categorical duality for certain classes of manysorted algebras, called many-sorted lattices because each sort admits a structure of distributive lattice. This duality is strongly based on the Priestley duality for distributive lattices developed in [3] and [4] and on the representation of many sorted lattices with operators given by Sofronie-Stokkermans in [6]. In this...

We introduce a new Priestley-style topological duality for N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to S. Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that we obtain a simple desc...

Abstract We provide a new perspective on extended Priestley duality for large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice operations are each presented as pair partial dual spaces. In enriched environment, equational conditions the algebraic side may more often be rendered first-order particular, we specialize our general results t...