Abstract Let and $H$?> be locally compact groups with fixed two-sided invariant Haar measures. A polyhomomorphism $G\rightarrowtail H$?> is a closed subgroup $R\subset G\times measure, whose marginals on are dominated by the measures . can regarded as multi-valued map sending points to sets equipped ‘uniform’ For two polyhomomorphisms ${G\rightarrowtail H}$?> $H\rightarrowtail K$?...