Dear Jaap, I also overlooked this email somehow. (-: On Thu, Jul 10, 2014 at 5:40 AM, Oosten, J. van <j.vanoosten@uu.nl> wrote:

is the following too simple-minded?

Given a well-founded poset (X,<), a category C and a function F which, to every functor G from an initial segment of X to C, assigns a cocone for G. Then there is a unique functor H:X-->C with the property that for every x\in X, H(x) is the vertex of the cocone which is F applied to the restriction of H to {y|y<x}.

I think my desired application is probably a bit more complicated than this, but if you have

...

a place where someone has written out exactly how to construct such a functor

for the simpler version, then I'd love to see it too! Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]