functors defined by well-founded induction

Suppose I have a well-founded poset W, regarded as a category, and I would like to define a functor W -> C into some other category by well-founded recursion. Is there written out anywhere in the literature a general schema for doing this? It's a little more subtle than defining an ordinary function by well-founded recursion, since we have to define the value of the functor on morphisms too, and its value at a given object may depend on its value at morphisms between previous objects. Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]