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.