The Chomsky-Schützenberger Theorem with Circuit Diagrams in the Role of Words

Guided by the idea of letters with finite lists of predecessors and successors, the paper develops the Chomsky-Schützenberger theorem for languages of arrows in any free prop with a finite set of generators on the positive integers. The setting of monoidal categories is essential to obtain a well-behaved generalization of rational set, from monoids to monoidal categories.