Related papers: A constructive Galois connection between closure a…
We study different notions of connected constructive metric spaces. They differ the types of connected components and how different components relate to each other. These notions are equivalent in classical point set topology but they give…
The concept of Galois connections (i.e., adjoint pairs between posets) is ubiquitous in mathematics. In representation theory, it is interesting because it naturally induces the adjoint quadruple between the categories of persistence…
The introduction of the categorical notion of closure operators has unified various important notions and has led to interesting examples and applications in diverse areas of mathematics (see for example, Dikranjan and Tholen (\cite{DT})).…
We present theoretical and practical results on the order theory of lattices of functions, focusing on Galois connections that abstract (sets of) functions - a topic known as higher-order abstract interpretation. We are motivated by the…
The Lambek-Grishin calculus is a symmetric extension of the Lambek calculus: in addition to the residuated family of product, left and right division operations of Lambek's original calculus, one also considers a family of coproduct, right…
Connection between the theory of aggregation functions and formal concept analysis is discussed and studied, thus filling a gap in the literature by building a bridge between these two theories, one of them living in the world of data…
In this paper we give a unified approach in categorical setting to the problem of finding the Galois closure of a finite cover, which includes as special cases the familiar finite separable field extensions, finite unramified covers of a…
We study four adjoint situations in pointfree topology that interchange images and preimages with closure and interior operators and establish with them a number of characterisations for meet-preserving maps, localic maps, open maps (in a…
Given a braided tensor *-category C with conjugate (dual) objects and irreducible unit together with a full symmetric subcategory S we define a crossed product C\rtimes S. This construction yields a tensor *-category with conjugates and an…
Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois…
In a 1985 commentary to his collected works, Kolmogorov remarked that his 1932 paper "was written in hope that with time, the logic of solution of problems [i.e., intuitionistic logic] will become a permanent part of a [standard] course of…
For a finite Galois extension K/k and an intermediate field F such that Gal(K/F) has a normal complement in Gal(K/k), we construct and characterize Hopf Galois structures on K/k which are induced by a pair of Hopf Galois structures on K/F…
We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H. We also show that Q-Galois subextensions are closed elements of the…
We consider $S$-operations $f \colon A^{n} \to A$ in which each argument is assigned a signum $s \in S$ representing a "property" such as being order-preserving or order-reversing with respect to a fixed partial order on $A$. The set $S$ of…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
These notes are an exposition of Galois Theory from the original Lagrangian and Galoisian point of view. A particular effort was made here to better understand the connection between Lagrange's purely combinatorial approach and Galois…
This article is interested in pullbacks under the logarithmic derivative of algebraic ordinary differential equations. In particular, assuming the solution set of an equation is internal to the constants, we would like to determine when its…
It is well-known fact that there exists 1-1 correspondence between so-called double (or flou) sets and intuitionistic sets (also known as orthopairs). At first glance, these two concepts seem to be irreconcilable. However, one must remember…
We investigate characterizations of the Galois connection sInv-Aut between sets of finitary relations on a base set A and their automorphisms. In particular, for A=omega_1, we construct a countable set R of relations that is closed under…
Formal concept analysis (FCA) is built on a special type of Galois connections called polarities. We present new results in formal concept analysis and in Galois connections by presenting new Galois connection results and then applying…