of this paper is to prevent the abstract data type researcher from an improper, naive use of category theory. We mainly emphasize some unpleasant properties of the synthesis functor when dealing with so-called loose semantics in a hierarchical approach. All our results and counter-examples are very simple, nevertheless they shed light on many common errors in the specification field. We also summarize some properties of the category of models "protecting predefined sorts." Keywords : abstract data types, abstract specifications, category theory, completeness, consistency, initial model, structured specifications.