D-inverse constellations

We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial algebras in the sense that they possess a partial product, and a unary operation $D$. We consider constellations in which elements have a suitable notion of inverse, giving the notion of a D-inverse constellation.