The Stone–Čech Compactification of Groupoids - Behrouzi, F. (Ukrains’kyi Matematychnyi Zhurnal, 2015)
Let $G$ be a discrete groupoid. Consider the Stone–Čech compactification $βG$ of $G$ . We extend the operation on the set of composable elements $G^{(2)}$ of $G$ to the operation * on a subset $(βG)^{(2)}$ of $βG×βG$ such that the triple $(βG, (βG)^{(2)}$, *) is a compact right topological semigroupoid.