[Haskell-cafe] map over Bijections

Hi. I need map equivalent for Bijection type which is defined in fclabels: data Bijection (~>) a b = Bij { fw :: a ~> b, bw :: b ~> a } instance Category (~>) => Category (Bijection (~>)) where ... I can define this function as follows: mapBij :: Bijection (->) a c -> Bijection (->) [a] [b] -> Bijection (->) [a] [c] mapBij b1 b = (map (fw b1)) `Bij` (map (bw b1)) but do I really need to do it explicitly? Can I obtain same result using some Category combinators or other common stuff? Sergey