Let's see if any of these are useful (a lot more at https://ghc.haskell.org/trac/ghc/ticket/13026)

(||||) :: (f a -> b) -> (g a -> b) -> ((Sum f g) a -> b) 

f |||| g = \case 

  InL fa -> f fa 

  InR ga -> g ga 

(&&&&) :: (a -> f b) -> (a -> g b) -> (a -> (Product f g) b) 

(f &&&& g) a = f a `Pair` g a 

I couldn't think of any for Data.Functor.Compose, names are up for bikeshedding