Related papers: Stone duality for spectral sheaves and the patch m…

We establish two duality theorems which refine the classical Stone duality between generalized Boolean algebras and locally compact Boolean spaces. In the first theorem we prove that the category of left-handed skew Boolean algebras whose…

We extend Stone duality to a fully faithful embedding of condensed sets into fpqc sheaves over an arbitrary field, which preserves colimits and finite limits. We study how familiar notions from condensed mathematics/topology and algebraic…

We extend Stone duality between generalized Boolean algebras and Boolean spaces, which are the zero-dimensional locally-compact Hausdorff spaces, to a non-commutative setting. We first show that the category of right-handed skew Boolean…

It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a…

We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A…

In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological…

There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…

We extend Priestley Duality to suitable categories of fuzzy topological spaces and ordered algebraic structures that generalize bounded distributive lattices. The duality we prove extends not only classical Priestley Duality between…

In this note we shall generalize the Stone duality between compact totally disconnected spaces and Boolean algebras to a duality between all complete non-Archimedean uniform spaces and Boolean algebras.

The term Stone-type duality often refers to a dual equivalence between a category of lattices or other partially ordered structures on one side and a category of topological structures on the other. This paper is part of a larger endeavour…

We prove three new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to the category of spectral spaces with decent lumps and with…

We show how Stone duality can be extended from maps to relations. This is achieved by working order enriched and defining a relation from A to B as both an order-preserving function from the opposite of A times B to the 2-element chain and…

We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

A convexity space is a set X with a chosen family of subsets (called convex subsets) that is closed under arbitrary intersections and directed unions. There is a lot of interest in spaces that have both a convexity space and a topological…

We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties

In this paper we provide a Stone style duality for monotone semilattices by using the topological duality developed in \cite{Celani2020} for semilattices together with a topological description of their canonical extension. As an…

We connect Priestley duality for distributive lattices and its generalization to distributive meet-semilattices to Hofmann-Mislove-Stralka duality for semilattices. Among other things, this involves consideration of various morphisms…

We carry out a systematic, topos-theoretically inspired, investigation of Wallman compactifications with a particular emphasis on their relations with Gelfand spectra and Stone-Cech compactifications. In addition to proving several specific…

We introduce a new topological encoding of executions of round-based, full-information distributed protocols via spectral spaces. Such protocols constitute a model of distributed computations which are functorially presented and englobe…