\documentclass[12pt]{article}
\usepackage{amsthm,amssymb,amsmath}
\usepackage{pgf,pgfplots,tikz}
%\pgfplotsset{width=7cm,compat=newest}
\usetikzlibrary{snakes,arrows,matrix,shapes,backgrounds}
\begin{document}
$$
\begin{tikzpicture}[thick,>=stealth,shorten >=2pt,looseness=.5,auto,descr/.style={fill=white}]
\matrix [matrix of math nodes,row sep=10mm,column sep=10mm]
{
|(1)|A&  |(2)|B&|(3)| C\\
|(4)|A&  |(5)|D&|(6)| E\\
&|(8)| F&|(9)|F\\
};
\begin{scope}[every
node/.style={sloped,midway,auto,font=\scriptsize}]
\draw [right hook->](1) -- node[] {} (2);
\draw [->](2) -- node[] {} (3);
\draw[double] (1) -- node[] {} (4);
\draw[->] (2) -- node[] {} (5);
\draw[->] (5) -- node[] {} (6);
\draw[->] (5) -- node[] {} (8);
\draw [->](6) -- node[] {} (9);
\draw [double](8) -- node[] {} (9);
\draw [->](3) -- node[] {} (6);
\draw [right hook->](4) -- node[] {} (5);
\end{scope}
\end{tikzpicture}
$$
\end{document}