In *Accessible categories : the foundations of categorical model theory*, chapter 3 p.58, Makkai and Paré claim that there is "an (obvious) identification of a class of sketches so that the categories Mod(S) for such sketches S are precisely the categories of models of complete theories with elementary embeddings as morphisms".

In other terms, there seems to be a "sketchable" counterpart of the property of completeness of a formal theory. But there is no explicit reference in the book.

What can be this sketch-theoretical property for such identification? Is there any paper where this identification is explicit?

Many thanks, in advance.