We show that recent big growth of applications of Category Theory to Physics might be associated with unavoidable appearance of model theoretical structures coming from formal languages used to describe mathematical models of so called physical reality. Even in the simplest case of Elementary Protocolar Theory we are (to fulfil the conditions of consistency and simplicity of the language) confined to some model theoretical limitations. We discuss some examples. We also formulate conjectures and perspectives for future investigations.

PACS numbers: 02.10.Ab, 03.65.Ca