What is common math notation for "fanout" combination of functions? Let's say we have $f_1 : A \to X$ and $f_2 : A \to Y$. What is the most canonical way to denote $f : A \to X \times Y$ that combines $f_1$ and $f_2$ by outputting pair of their respective values for same argument? Sort of like this haskell operation. For sure mathematicians must have some shortcut for such common operation.

My Personally choice is: $[f_1,f_2]$.

And by introducing I would always mention that it is the unique function $A\to X\times Y$ determined by $p_i\circ[f_1,f_2]=f_i$ for $i=1,2$ where the $p_i$ denote the projections.

Moreover it cannot harm to mention that the function is prescribed by: $$a\mapsto\langle f_1(a),f_2(a)\rangle$$

In my view curled brackets are "overcharged" in mathematics, and I try to withold that a bit :-).