How do I denote that I am aggregating values into a vector?
For example, I have a set of values $F$ in which a function $fun$ will be applied. Finally, a vector is build with the results.
For example, if $F = \{a,b\}$ and $fun(a) = 1, fun(b) = 2$, how can I denote that I'm assembling the vector: [1 2]?
Will a cartesian product suffice?
$$ V = \prod_{e \in F} fun(e) $$
Or should I use other operation?
You may want to order the elements of $F$ into a given vector $\mathbf{f} \in F^n$, where $F^n = F \times F \times ... \times F$ $n$ times (that is, if the elements of $F$ are distinct; otherwise you are using a multiset). This will allow for a reasonable input representation for a vector-valued function.
To indicate that you are assembling a vector, you may want to establish a vector-valued function $\mathbf{v} : F^n \rightarrow \mathbb{R}^n$ that is defined such that
$$\mathbf{v}_i(\mathbf{f}) = fun(\mathbf{f}_i), i \in [n].$$
This is a reasonable way to indicate that you are assembling a vector using the output of the function $\mathbf{v}$.