In this paper we are concerned with the notion of language and its relation to category theory. Our motivations has been Farisse's treatment of formulas as operators. We show that the formulas of first order language with finitely many predicates can be (naturally) characterized as class of functiors from one category to another.

No abstract do artigo consta: "Let r be a finite relational type. The space Str(r) of all structures of type r is naturally equipped with a pseudometric, by saying that the distance of two structures is equal to 1/(1+r) iff a sentence of quantifier rank r can separate the two structures, with r minimal. In this self-contained paper, we give a simple prrof of the convergence of every Cauchy sequence structures of type r. The compactness of Str (r) now follows from an elementary topological argument."