Related papers: Stone duality of Lawson compact algebraic L-domain
In a finite distributive lattice $\L$ we define two functions $s(\alpha)=|\{\delta \in \mathcal{L} | \delta \leq \alpha \}|$ and $l(\alpha)=|\{\delta \in \mathcal{L} | \delta \geq \alpha \}|$. In this present article we prove that the sum…
For a finite lattice L, the congruence lattice Con L of L can be easily computed from the partially ordered set J(L) of join-irreducible elements of L and the join-dependency relation D\_L on J(L). We establish a similar version of this…
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
We extend the Stone duality between topological spaces and locales to include order: there is an adjunction between the category of preordered topological spaces satisfying the so-called open cone condition, and the newly defined category…
We describe the approach to lattice extraction of Generalized Parton Distributions (GPDs) that is based on the use of the double distributions (DDs) formalism within the pseudo-distribution framework. The advantage of using DDs is that GPDs…
As was shown by a part of the authors, for a given $(2, 3, 5)$-distribution $D$ on a $5$-dimensional manifold $Y$, there is, locally, a Lagrangian cone structure $C$ on another $5$-dimensional manifold $X$ which consists of abnormal or…
We propose some analogue of the Narain lattice for CHL string. The symmetries of this lattice are the symmetries of the perturbative spectrum. We explain in this language the known results about the possible gauge groups in compactified…
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial…
A preordered topological space is a topological space with a preordering. We exhibit a Stone-like duality for preordered topological spaces, Inspired by a similar duality for bitopological spaces, due to Jung-Moshier and Jakl, and by a…
We describe a duality for quantale-enriched categories that extends the Lawson duality for continuous dcpos: for any saturated class J of modules that commute with certain weighted limits, and under an appropriate choice of morphisms, the…
We introduce the notion of crystallographic T-duality, inspired by the appearance of $K$-theory with graded equivariant twists in the study of topological crystalline materials. Besides giving a range of new topological T-dualities, it also…
De Vries duality yields a dual equivalence between the category of compact Hausdorff spaces and a category of complete Boolean algebras with a proximity relation on them, known as de Vries algebras. We extend de Vries duality to completely…
We investigate categories in which products distribute over coproducts, a structure we call doubly-infinitary distributive categories. Through a range of examples, we explore how this notion relates to established concepts such as…
We formulate a fracton-elasticity duality for twisted moir\'e superlattices, taking into account that they are incommensurate crystals with dissipative phason dynamics. From a dual tensor-gauge formulation, as compared to standard crystals,…
A variant of the topological twist, involving SL(2,Z) dualities and hence named topological duality twist, is introduced and explicitly applied to describe a U(1) N=4 super Yang-Mills theory on a Kaehler space with holomorphically…
In this article we prove a set of preservation properties of the reticulation functor for residuated lattices (for instance preservation of subalgebras, finite direct products, inductive limits, Boolean powers) and we transfer certain…
In the second edition of the congruence lattice book, Problem 22.1 asks for a characterization of subsets $Q$ of a finite distributive lattice $D$ such that there is a finite lattice $L$ whose congruence lattice is isomorphic to $D$ and…
In this paper subvarieties of pseudocomplemented distributive lattices are classified by their unification type. We determine the unification type of every particular unification problem in each subvariety of pseudocomplemented distributive…
Divisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek's basic logic with an important significance in the study of fuzzy logic. The purpose of this paper is to investigate commutative…
We generalize our previous lattice construction of the abelian bosonization duality in $2+1$ dimensions to the entire web of dualities as well as the $N_f=2$ self-duality, via the lattice implementation of a set of modular transformations…