larry harper asked me about a certain concept of morphism between directed graphs that he's trying to invent, motivated in a certain way by the idea of "circuit elements connected in series or in parallel analyzable as a single compound circuit element" (or something like that); he wants to find out to what extent it's already been invented. i told him that i'd think about it a bit, and that there ought to be some nice ways of thinking about it...

somehow what harper's trying to do vaguely reminds me of joyal's category of n-stage trees... or something like that... ???...

??perhaps we should try developing harper's category as fibered over a category of vertex sets and partial maps... ??or something like that??