Diagramme commutatif pour la limite inductive

\begin{tikzpicture}
% La grille à commenter
%\draw [help lines] (-2,0) grid (2,4);
% Positionner les noeuds
\node (Xi) at (-2,4)  {$X_i$};
\node (Xj) at (2,4)  {$X_j$};
\node (X) at (0,2)  {$X$};
\node (Y) at (0,0)  {$Y$};
% Tracer les flèches et leurs label
\draw [->,>=latex] (Xi) -- (Xj) node[midway,above]{$f_{ij}$};
\draw [->,>=latex] (Xi) -- (X) node[midway,above right]{$\phi_i$};
\draw [->,>=latex] (Xj) -- (X) node[midway,above left]{$\phi_j$};
\draw [->,>=latex] (Xi) -- (Y) node[midway,below left]{$\psi_i$};
\draw [->,>=latex] (Xj) -- (Y) node[midway,below right]{$\psi_j$};
\draw [->,>=latex] (X)  -- (Y) node[midway,above right]{$u$};
\end{tikzpicture}