[Haskell-beginners] Question on terminology

[Joel Neely]

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
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