Let $$f : X_0 \rightarrow Y_0, \;\;\; g:X_1 \rightarrow Y_1$$ and define that the "direct product" of $f$ and $g$ is a map $$f \otimes g : (X_0 \times X_1) \rightarrow (Y_0 \times Y_1), \mbox{ such that } (f \otimes g)(x_0,x_1)=(f(x_0),g(x_1)).$$

Question 1. What is the standard terminology/notation for this concept?

Now given a function $h$, it's possible that $h$ has the property that there exist $f$ and $g$ such that $$h = f \otimes g$$ Question 2. What is the name of this property?