\documentclass{amsart}
\usepackage{amsmath,amssymb,nopageno}
\usepackage[all]{xy}
\begin{document}
 \begin{equation*}
  \xymatrix@C+2em@R+2em{
   F(X) \ar[rr]^*{F(f)} & & F(Y) \\
   & L \ar@{<-}[ul]^(0.4)*-<1ex,1ex>{\phi_X} \ar@{<-}[ur]_(0.4)*-<1ex,1ex>{\phi_Y} & \\
   & N \ar@{<-}@/^10pt/[uul]^*{\psi_X} \ar@{<-}@/_10pt/[uur]_*{\psi_Y} \ar@{<--}[u]|*+<5pt,5pt>{u} &
  }
 \end{equation*}
\end{document}

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