On pages 205ff of "Seven Sketches", Brendan Fong und David Spivak show an example how a closed electric circuit with several valued elements and 4 ports can be considered as a morphism. They wrote: "We do this by marking the ports in the interface using functions from finite sets". Then they draw an one-element input set and a two-element output set and map these onto two arbitrary ports of the circuit. The question is, why they don't take a 256-element input set and a 7-element output set, and why they map the input set just to this port and not to another one (in "A compositional Framework for Reaction Network" John Baez and Blake Pollard give an example of a reaction Petri net that is a morphism from the empty set into itself).

In the example the circuit is an element of Hom[1,2] (1 und 2 mean the one-element or 2-element set respective), but it could might just as well be an element of Hom[256,7] or of Hom[0,0]. Is this indeed the intention?

In the example the circuit is an element of Hom[1,2] (1 und 2 mean the one-element or 2-element set respective), but it could might just as well be an element of Hom[256,7] or of Hom[0,0]. Is this indeed the intention?