Adjunction space diagram

\documentclass[a4paper,11pt]{scrartcl}
\usepackage{tikz}
\usetikzlibrary{matrix,arrows,decorations.pathmorphing}

\begin{document}

\begin{center}
\begin{tikzpicture}
\node (1) at (0,0) {$A$};
\node (2) at (4,0) {$Y$};
\node (3) at (0,-2) {$X$};
\node (4) at (4,-2) {$X \cup Y$};
\node (5) at (6,-3) {$X \cup_f Y$};
\path[->]
(1) edge node[above]{$f$} (2)
(3) edge [bend right] node[above]{$\bar f$} (5)
(4) edge node[below]{$\pi$} (5);
\path[right hook->]
(1) edge (3)
(3) edge (4)
(2) edge (4)
(2) edge [bend left] (5);
\end{tikzpicture}
\end{center}

\end{document}