[Haskell-cafe] Name My Functor Classes

[Ashley Yakeley]

These classes seem like they might correspond to concepts in category 
theory:

    class Functor f where
        fmap :: (a -> b) -> f a -> f b
    -- must satisfy:
    --   fmap id = id
    --   fmap (p . q) = (fmap p) . (fmap q)

    class (Functor f) => C1 f where
        f1 :: f (a -> b) -> f a -> f b

    class (C1 f) => C2 f where
        return :: a -> f a
    -- must satisfy:
    --   fmap = f1 . return

    class (C2 f) => Monad f where
        (>>=) :: f a -> (a -> f b) -> f b
    -- must satisfy:
    --   fmap ab fa = fa >>= (return . ab)
    --   f1 fab fa = fab >>= (\ab -> fmap ab fa)
    --   (return a) >>= p = p a
    --   (fa >>= p) >>= q = fa >>= (\a -> p a >>= q)

What are good names for C1, C2 and f1?

-- 
Ashley Yakeley, Seattle WA