D-inverse constellations

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, University of York, York, YO10 5GH, United Kingdom

2 Mathematics, School of Computing and Mathematical Sciences, University of Waikato, Hamilton, New Zealand

10.48308/cgasa.2025.236863.1519

Abstract

Constellations are partial algebras in the sense that they possess a partial product, and a unary operation modelling domain.  They were first used to give an ESN-style theorem for left restriction semigroups in terms of so-called inductive constellations.  Here, we consider constellations in which elements have a suitable notion of inverse, giving the notion of a D-inverse constellation.  We show that there is a categorical isomorphism between the category of ordered groupoids and the category of D-inverse constellations.  This may be viewed as a generalisation of the ESN theorem, which relates the category of inductive groupoids to the category of inverse semigroups.

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References

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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 05 October 2025

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