Let's say I have some map $f$ that'll take a tuple with element types $A, B$ and $C$ to some type $T$
$f (x,y,z): A \times B \times C \rightarrow T$
and then say we have a map $g$, that takes an element $A$ and returns a map $h$, which takes a tuple of $B$ and $C$ to the same $T$.
$g (x): A \rightarrow \{h (y,z): B \times C \rightarrow T\}$
and let $f(x,y,z) = g(x)(y,z)$ for all $(x,y,z)$ in $A \times B \times C$
What's the name of the relationship $g$ has to $f$, or the name of the operation that produces $g$ from $f$? What sort of a thing is it?
I think it might be a lift but I'm not sure if I've understood what a lift is.