What is a function $g$ called, which, composed with a certain function $f_2$, yields a given function $f_1$ (i.e. $f_1 = f_2\circ g$)?

Question

Let $X_1$, $X_2$, and $Y$ be non-empty sets. Let $f_1:X_1\rightarrow Y$ and let $f_2:X_2\rightarrow Y$. What's the terminology for a function $g:X_1\rightarrow X_2$ that satisfies: $f_1 = f_2\circ g$? This concept reminds me a little bit of category theory's functors, but since I know barely any category theory, I'm not sure. Alternatively, it reminds me of a divisor in some algebraic structure.

Answer 1

You can say that "$g$ witnesses that $f_1$ factors through $f_2$", or a variation of that.