Diagram
[ilmath]\begin{xy}
\xymatrix{
& & \prod_{\alpha\in I}X_\alpha \ar[dd] \\
& & \\
Y \ar[uurr]^f \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@{>}_{f_c,\ f_b,\ f_a} "x3"+<0.9ex,0.3ex>; "3,1";
\restore
}
\end{xy}[/ilmath]

TODO: Caption

TODO: Fix up diagram a bit?