so is there a nice "algebraic stack" (or something...) of "representations of quiver q" or something like that?? ...one reason that i'm thinking about this at the moment is that we're maybe seeing some sort of "weil conjectures" stuff going on in connection with quiver representations, and i'm trying to understand in what context this should be placed... perhaps a fairly standard algebraic geometry context if there's a certain nice algebraic stack here... or something like that...

let's take for example q = a->b->c ...

let's try to formulate this as a tensor-products-and-finite-colimits theory...

well, so there's the free finitely cocomplete symmetric monoidal algebroid on the quiver algebroid... which is something we've probably thought about before... and we're thinking about it again, maybe from a slightly new viewpoint... or maybe it's really the same viewpoint and i just didn't recognize it...

??explicit description of the syntactic algebroid?? ...