Is there a technical name for a function $f$ such that $(g \circ f)(a_1, a_2,\cdots) \rightarrow g(a_1, a_2, \cdots)$? That is, is there a name for a function $f$ such that the result of composing $g$ with $f$ is $g$ invoked with $f$'s arguments?
EDIT: Accidentally reversed the order of operations and put $f \circ g$ when I meant $g \circ f$ (i.e. $g(f(\cdots)$).