\documentclass[a4paper,12pt]{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage{tikz}
\begin{document}

\begin{center}
\tikzset{node distance=2cm, auto}
\begin{tikzpicture}[line width=.5pt]%[style={very thick}]
  \node (a1) {$0$};
    \node (a2) [right of=a1] {$M^u$};
  \node (a3) [right of=a2] {$P^v$};
  \node (b2) [below of=a2] {$F^v$};
  \draw[->] (a1) -- (a2);
    \draw[->] (a2) to node  {$\varphi^*$} (a3);
    \draw[->] (a3) to node  {$g$} (b2);
    \draw[->] (a2) to node[swap] {$f^*$}  (b2); 
    \draw(7,-1) node {$ \phi^* = \Hom \left(\phi, E\big(\dfrac{R}{m}\big) \right)$}
\end{tikzpicture}
\end{center}

\end{document}