D-inverse constellations

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.