How to denote a function mapping of two parameters to an output? I am wondering how to denote something like this:
I have a function mapping two sets to a set of vectors and am currently denoting it as so:
$p: [F, \Sigma] \to S $
I am wondering if this is correct, and if not, what is? 
I am a computer science student and did a year of mathematics at degree level, but that was a long time ago and I have forgotten a lot of the basics. 
If I am wrong I would appreciate a semi in depth answer as to why.

A function mapping two arguments from $A$ and $B$ respectively to $C$ is denoted
$$f:A\times B\to C,$$
where $\times$ here denotes the Cartesian product.
