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$$
\Dg
F\times K\times U     & \rTo ^{\rm proj}     &           & K\times U        \\
\dTo                  &                      &           & \dTo >{\rm proj} \\
F\times_K (K\times U) & {} \approx F\times U & \rTo ^{\rm proj}& U          \\
\endDg
$$