[Haskell-beginners] Question on terminology

IIUC, one would describe fmap as "lifting" a function g into a functor f, in the sense of Functor f => (g a b) -> g a -> g b Is there an inverse concept (? co-lift ?) that describes Functor f => (g a -> g b) -> a -> b Similarly is there standard terminology for "distributing" and "gathering" in the sense of Functor f => f [a] -> [f a] and Functor f => [f a] -> f [a] respectively? References much appreciated! -jn- -- Beauty of style and harmony and grace and good rhythm depend on simplicity. - Plato