\ It is sometimes necessary to name the edges in a drawing. We may then adopt the convention sometimes used for drawing diagrams in a category: the bullets are replaced by the names of the corresponding nodes, and arrows are interrupted to write their name at a place free from crossing, as in

\ Note that no confusion is possible between the names of nodes and those of other edges, e.g., in

\ it is clear that x and z are nodes since arrow tips point to them, and that y is the name of an edge of length 3.

\ One particularity of monographs is that edges can be adjacent to themselves, as in

\ Of course, knowing that a is a morphism sometimes allows to deduce the type of an edge, possibly from the types of adjacent edges. In the present case, indicating a single type would have been enough to deduce all the others.

\ In particular applications it may be convenient to adopt completely different ways of drawing (typed) monographs.

6 Graph Structures and Typed Monographs

\ \ \

\ \ The next lemma is central as it shows that no graph structure is omitted by the functor S if we allow sort-preserving isomorphisms of graph structures. We assume the Axiom of Choice through its equivalent formulation known as the Numeration Theorem [5].

\ \