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140437 - Groupoids on a skew lattice of objects.pdf (366.61 kB)

Groupoids on a skew lattice of objects

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posted on 2023-05-20, 16:59 authored by Desmond FitzGeraldDesmond FitzGerald
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.

History

Publication title

Art of Discrete and Applied Mathematics

Article number

03

Number

03

Pagination

1-14

ISSN

2590-9770

Department/School

School of Natural Sciences

Publisher

Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska

Place of publication

Slovenia

Rights statement

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

Repository Status

  • Open

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Expanding knowledge in the mathematical sciences

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