Ubiquitous and Pervasive Computing, and the Internet of Things, promote dynamic interaction among heterogeneous systems. To achieve this vision, interoperability among heterogeneous systems represents a key enabler, and mediators are often built to solve protocol mismatches. Many approaches propose the synthesis of mediators. Unfortunately, a rigorous characterization of the concept of interoperability is still lacking, hence making hard to assess their applicability and soundness. In this paper, we provide a framework for the synthesis of mediators that allows us to: (i) characterize the conditions for the mediator existence and correctness; and (ii) establish the applicability boundaries of the synthesis method.