Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 24 1 2026 01 01 D-inverse constellations 1 28 106295 10.48308/cgasa.2025.236863.1519 EN Victoria Gould Department of Mathematics, University of York, York, YO10 5GH, United Kingdom Timothy Stokes Mathematics, School of Computing and Mathematical Sciences, University of Waikato, Hamilton, New Zealand 0000-0003-2908-8563 Journal Article 2024 09 10 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. https://cgasa.sbu.ac.ir/article_106295_d17dc1fe0d8c0a8bd81d05587a73d9d0.pdf