Related papers: Stone Duality for Relations
Duality, the equivalence between seemingly distinct quantum systems, is a curious property that has been known for at least three quarters of a century. In the past two decades it has played a central role in mapping out the structure of…
We answer an open question in the theory of transducer degrees initially posed in [1] on the existence of a diamond structure in the transducer hierarchy. Transducer degrees are the equivalence classes formed by word transformations which…
A double category of relations is essentially a cartesian equipment with strong, discrete and functorial tabulators and for which certain local products satisfy a Frobenius Law. A double category of relations is equivalent to a double…
Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants…
We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms…
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling…
We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in…
The aim of this work is to further develop the calculus of (internal) relations for a regular Ord-category C. To capture the enriched features of a regular Ord-category and obtain a good calculus, the relations we work with are precisely…
We provide a definition of enrichment that applies to a wide variety of categorical structures, generalizing Leinster's theory of enriched $T$-multicategories. As a sample of newly enrichable structures, we describe in detail the examples…
Duality is the operation that interchanges hypervertices and hyperfaces on oriented hypermaps. The duality index measures how far a hypermap is from being self-dual. We say that an oriented regular hypermap has \emph{duality-type} $\{l,n\}$…
The (A,D) duality pairs play crucial role in the theory of general relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems…
In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…
The familiar adjunction between ordered sets and completely distributive lattices can be extended to generalised metric spaces, that is, categories enriched over a quantale (a lattice of "truth values"), via an appropriate distributive law…
The notion of degree begins in field theory as the dimension of a field extension. In algebraic geometry, this idea reappears as the degree of a finite morphism, defined using the induced extension of function fields. For proper morphisms…
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…
In this paper we introduce the concept of MV-topology, a special class of fuzzy topological spaces, and prove a proper extension of Stone Duality to the categories of limit cut complete MV-algebras and Stone MV-spaces, namely,…
We apply a recent duality theorem for tangles in abstract separation systems to derive tangle-type duality theorems for width-parameters in graphs and matroids. We further derive a duality theorem for the existence of clusters in large data…
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…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph which contains a…