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Groupoids on a skew lattice of objects

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FitzGerald, DG 2019 , 'Groupoids on a skew lattice of objects' , Art of Discrete and Applied Mathematics, vol. 2, no. 2 , pp. 1-14 , doi: 10.26493/2590-9770.1342.109.

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Abstract

Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad theorem, we consider a groupoid (small category of isomorphisms) in which the set of objects carries the structure of a skew lattice. The objects act on the morphisms by left and right restriction and extension mappings of the morphisms, imitating those of an inductive groupoid. Conditions are placed on the actions, from which pseudoproducts may be defined. This gives an algebra of signature (2, 2, 1), in which each binary operation has the structure of an orthodox semigroup. In the reverse direction, a groupoid of the kind described may be reconstructed from the algebra.

Item Type: Article
Authors/Creators:FitzGerald, DG
Keywords: inductive groupoids, skew lattices, orthodox semigroups
Journal or Publication Title: Art of Discrete and Applied Mathematics
Publisher: Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska
ISSN: 2590-9770
DOI / ID Number: 10.26493/2590-9770.1342.109
Copyright Information:

Licensed under Creative Commons Attribution 4.0 International (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/

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