\dvips
\usepackage[small,nohug]{diagrams} % nohug: don't rotate labels on diagonal arrows

\diagram{
FX  & \rDashto^{\bar f}                & A  \\
UFX & \rTo^{U\bar f}                   & UA \\
    & \luTo(1,2)_{\eta_X} \ruTo(1,2)_f &    \\
    & X                                &
}