Galois connection for sets of operations closed under permutation, cylindrification and composition

We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a Galois connection between operations and systems of pointed multisets, and we also describe the closed sets of the dual o...

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Bibliographic Details
Published inarXiv.org
Main Authors Couceiro, Miguel, Lehtonen, Erkko
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.09.2010
Subjects
Composition
Mathematics - Rings and Algebras
Permutations
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Summary:We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a Galois connection between operations and systems of pointed multisets, and we also describe the closed sets of the dual objects by means of necessary and sufficient closure conditions. Moreover, we show that the corresponding closure systems are uncountable for every A with at least two elements.
ISSN:2331-8422
DOI:10.48550/arxiv.0910.5409