Monoid

Monoid.tex

\begin{tikzpicture}
\matrix (m) [matrix of math nodes,row sep=3em,column sep=8em,minimum width=2em]
 {
             & \bullet \\
     \bullet & \bullet \\
             & \bullet \\};

\path[->] (m-2-1) edge [in=70,out=100,loop] node[auto](F) {$f$} ();
\path[->,draw] (m-2-1) edge  [in=60,out=120,loop,distance=2cm] node[auto](G) {$g$} (m-2-1);
\path[->,draw] (m-2-1) to  [in=40,out=140,loop,distance=4.5cm] node[auto](GCF) {$g\circ f$} (m-2-1);
\path[->,draw] (m-2-1) edge  [in=-40,out=225,loop,distance=1.5cm] node[below] {$id_M$} (m-2-1);
\path[->] (F) edge[bend right,dashed] (m-3-2);
\path[->] (G) edge[dashed] (m-2-2);
\path[->] (GCF) edge[bend left,dashed] (m-1-2);
\draw(1.5,0) ellipse (1cm and 2cm) node[right=1cm] {$Hom(\mathcal{M})$};
\end{tikzpicture}