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