# Galois Connections for Operations and Relations

@inproceedings{Pschel2004GaloisCF, title={Galois Connections for Operations and Relations}, author={Reinhard P{\"o}schel}, year={2004} }

This paper reports on various Galois connections between operations and relations. Several specifications and generalizations are discussed.

## 43 Citations

### Function classes and relational constraints stable under compositions with cloness

- MathematicsDiscussiones Mathematicae - General Algebra and Applications
- 2009

The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.

### Connections arising in Clone Theory (Algebra and Computer Science)

- Mathematics
- 2018

Galois connections appear in various areas in mathematics and computer science. In this article a brief review is presented on Galois connections arising in clone theory.

### Basics of Galois Connections

- MathematicsComplexity of Constraints
- 2008

Basic properties of Galois connections between sets of relations and sets of functions or generalized functions are given and some tools for the representation of several closure operators on relations as closure operators of some Galois connection are provided.

### Invariance groups of functions and related Galois connections

- MathematicsBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- 2020

Invariance groups of sets of Boolean functions can be characterized as Galois closures of a suitable Galois connection. We consider such groups in a much more general context using group actions of…

### Completeness Criteria and Invariants for Operation and Transformation Algebras

- Mathematics
- 2004

Operation algebras serve as representations of composition algebras (in the sense of Lausch/Nobauer). In this paper they are described and characterized by invariant relations as Galois-closed sets…

### On closed sets of relational constraints and classes of functions closed under variable substitutions

- Mathematics
- 2005

Abstract.Pippenger’s Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set A and taking…

### Reflections on and of minor-closed classes of multisorted operations

- MathematicsAlgebra universalis
- 2018

The minor relation of functions is generalized to multisorted functions. Pippenger’s Galois theory for minor-closed sets of functions is extended to multisorted functions and multisorted relation…

### Clausal relations and C-clones

- Mathematics
- 2010

We introduce a special set of relations called clausal relations. We study a Galois connection Pol−C Inv between the set of all finitary operations on a finite set D and the set of clausal relations,…

### CONTRIBUTIONS TO GENERAL ALGEBRA xx

- Mathematics
- 2006

In this paper we describe binary relations σ ⊆ A × A preserved by the endomorphisms of a quasiorder q ⊆ A × A, i.e. with the property End q ⊆ End σ. In particular we determine the quasiorder lattice…

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Operation algebras serve as representations of composition algebras (in the sense of Lausch/Nobauer). In this paper they are described and characterized by invariant relations as Galois-closed sets…

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