On Monographs, Monadic Many-Sorted Algebras and Graph Structures

A simple notion of monograph is proposed that generalizes the standard notion of graph and can be drawn consistently with them. It is shown that monadic many-sorted signatures can be represented by monographs, and that the corresponding algebras are isomorphic to the monographs typed by the corresponding signature monograph. Monographs therefore provide a simple unifying framework for working with monadic algebras. The simplicity of monographs is illustrated by deducing some of their categorial properties from those of sets