Is there anything known about the following type of problem. Let F,G : C -> D be functors and let E be a subcategory of C and let F' G' be the restirctions of F and G to E. Let a' : F' -> G' be a natural transformation. When does there exist a natural transformation alpha : F -> G that extends alpha' so that alpha restricted to E is equal to alpha'? What if E is a set of generators for C? Thanks Per K. Jakobsen