Differentiating folds?

Has anyone ever worked out what it means (or should mean) for a homomorphism f:(A,a) -> (B,b) between F-algebras to be differentiable? Analogies to other settings in which derivatives can be defined makes me believe that the result should be a morphism f' between two F'-algebras. When F is a polynomial functor, napkin-level-mathematics indicates this isn't completely wrong... Jacques [For admin and other information see: http://www.mta.ca/~cat-dist/ ]