[Haskell-cafe] General Functor and Traversable

Consider this: class (Category c, Category d) => Functor c d f where map :: c a b -> d (f a) (f b) Clearly mapM of Traversable is simply map :: Kleisli m a b -> Kleisli m (f a) (f b). But what is traverse? can it be so defined? I am thinking no, as Kleisli composition is not defined in general, but I know very little category theory so I may easily be wrong.