{$m=$};
\draw[braid] (s1t) to[out=270,in=180] (m) to[out=0,in=270] (s2t);
\draw[braid] (m) to (sb) ;
\end{tikzpicture}~~~~
\quad
\begin{tikzpicture} \path (0,0) node[empty,name=s1t] {}
(1,0) node[empty,name=s2t]  {} 
(0.5,0.5) node[empty,name=m] {} 
(0.5,1) node[empty,name=sb] {}
(1.5,0.5) node{} ;
\path (-0.5,0.5) node {$d=$};
\draw[braid] (s1t) to[out=90,in=180] (m) to[out=0,in=90] (s2t);
\draw[braid] (m) to (sb) ;
\end{tikzpicture}~~~~
\quad
\begin{tikzpicture} \path (0,1) node[empty,name=s1t] {}
(0,0.3) node[empty,name=e] {$\circ$} 
(0.0,0) node[empty,name=sb] {}
(1.0,0.5) node{} ;
\path (-0.5,0.5) node {$e=$};
\draw[braid] (s1t) to (e);
\end{tikzpicture}~~~~
\quad
\begin{tikzpicture} \path (0,1) node[empty,name=s1t] {}
(1,1) node[empty,name=s2t] {}
(0,0) node[empty,name=s1b] {}
(1,0) node[empty,name=s2b] {}
(1.5,0.5) node{} ;
\path (-0.5,0.5) node {$b=$};
\draw[braid] (s2t) to (s1b);
\fill[white] (0.5,0.5) circle (0.1);
\draw[braid] (s1t) to (s2b);
\end{tikzpicture} .$$

The fusion equation follows by the calculation

$$\begin{tikzpicture}[every node/.style={empty}]     \path (0.25,2.0) node[name=s1t] {}
(0.75,2.0) node[name=s2t] {}
(1.5,2.0) node[name=s3t] {}
(-0.25,0) node[name=s1b] {} 
(0.25,0) node[name=s2b] {}
(1.0,0) node[name=s3b] {};
\path (0.75,1.6) node[name=d1] {}
(0.25,1.2) node[name=d2] {} 
(0.0,0.8) node[name=d3] {};
\path (1.25,1.2) node[name=m1] {}
(1.0,0.4) node[name=m3] {}
(0.25,0.4) node[name=m2] {} ;
\draw[braid] (s2t) to[out=270,in=90] (d1); 
\draw[braid] (s3t) to[out=270,in=0] (m1) to[out=180,in=0] (d1) ;
\draw[braid] (m2) to (s2b);
\draw[braid] (m3) to (s3b);
\draw[braid] (s1t) to (d2);
\path[braid, name path=y] (m1) to[out=270,in=0] (m3) to[out=180,in=0] (d2) to[out=180,in=90] (d3);
\draw[braid, name path=x] (d1) to[out=180,in=0] (m2) to[out=180,in=0] (d3) to[out=180,in=90] (s1b);
\fill[white, 