If you're going to update transformers, could you perhaps export fstP and sndP from Product? I keep having to redefine them. And perhaps also a function dual to coproduct of type (a -> f b) -> (a -> g b) -> a -> Product f g b. Here's an example where they are very useful: {-# LANGUAGE MultiParamTypeClasses, UndecidableInstances #-} import Data.Functor.Product import Data.Functor.Coproduct import Data.Functor.Adjunction fstP :: Product f g a -> f a fstP (Pair x _) = x sndP :: Product f g a -> g a sndP (Pair _ x) = x productP :: (a -> f b) -> (a -> g b) -> a -> Product f g b productP f g a = Pair (f a) (g a) instance (Adjunction f g, Adjunction f' g') => Adjunction (Coproduct f f') (Product g g') where unit = productP (leftAdjunct left) (leftAdjunct right) counit = coproduct (rightAdjunct fstP) (rightAdjunct sndP) leftAdjunct f = productP (leftAdjunct (f . left)) (leftAdjunct (f . right)) rightAdjunct f = coproduct (rightAdjunct (fstP . f)) (rightAdjunct (sndP . f)) greetings, Sjoerd