I'm searching for an accepted name for the operation mapping two relations $R \subseteq X \times Y$ and $S \subseteq X \times Z$ to:
$$\{(u, v) \mid (\exists s)[(s, u) \in R \land (s, v) \in S]\} = S \circ R^{-1} \subseteq Y \times Z\enspace.$$
I wish to avoid the use of inverse here, expressing this as, for instance, $R \mathop{\text{sync}} S$, meaning that we do a synchronization on the first component.
Edit: even if this has no specialized name, I'm interested in papers that heavily rely on this operation.