t; x, &lt;x, y&gt; ~&gt; y of the product on its &quot;axes&quot;
| X and Y are functions p : X x Y -&gt; X, q : X x Y -&gt; Y.
| Any function h : W -&gt; X x Y from a third set W is uniquely
| determined by its composites p o h and q o h.  Conversely,
| given W and two functions f and g as in the diagram below,
| there is a unique function h which makes the diagram commute;
| namely, hw = &lt;fw, gw&gt;:
|
|
|                        W
|                        o
|                       /|\
|                