This diagram is identical to the Characteristic property of the product topology diagram - why!? Because they're both instances of a categorical product!
| [ilmath]\begin{xy}
\xymatrix{
& & \prod_{\alpha\in I}M_\alpha \ar[dd] \\
& & \\
M \ar[uurr]^\varphi \ar[rr]+<-0.9ex,0.15ex>|(.875){\hole} & & X_b
\save
(15,13)+"3,3"*+{\ldots}="udots";
(8.125,6.5)+"3,3"*+{X_a}="x1";
(-8.125,-6.5)+"3,3"*+{X_c}="x3";
(-15,-13)+"3,3"*+{\ldots}="ldots";
\ar@{->} "x1"; "1,3";
\ar@{->}_(0.65){\pi_c,\ \pi_b,\ \pi_a} "x3"; "1,3";
\ar@{->}|(.873){\hole} "x1"+<-0.9ex,0.15ex>; "3,1";
\ar@{->}_{\varphi_c,\ \varphi_b,\ \varphi_a} "x3"+<-0.9ex,0.3ex>; "3,1";
\restore
}
\end{xy}[/ilmath]
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TODO: Description
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