How do you express a function, whos range is a set of functions in math notation?

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I'm struggling to clearly express this notion. I would like to express a function of 2 variables as a successive application of 2 functions, first a function A->Fa that is mapped to a set of functions (mapping the sets B->C)

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The set of functions from $B$ to $C$ is denoted with $C^B$.

Thus :

$f : A \to C^B$.