--- a/text/appendixes/comparing_defs.tex Sat Dec 10 23:46:22 2011 -0800
+++ b/text/appendixes/comparing_defs.tex Sat Dec 10 23:46:30 2011 -0800
@@ -424,11 +424,13 @@
\end{figure}
In the first step we have inserted a copy of $(x\times I)\times I$.
Figure \ref{fzo4} shows the other case.
+
+\newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}}
+
\begin{figure}[t]
\centering
\begin{tikzpicture}
-\newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}}
\newcommand{\nsep}{1.8}
\clip (-4,-1.25)--(12,-1.25)--(16,1.25)--(-1,1.25)--cycle;
@@ -661,13 +663,58 @@
\end{figure}
Given 1-morphisms $a$, $b$ and $c$ of $D$, we define the associator from $(a\bullet b)\bullet c$ to $a\bullet(b\bullet c)$
-as in Figure \nn{like triangle 4.a, but more general; use three colors as in that fig}.
+as in Figure \ref{fig:associator}.
This is just a reparameterization of the pinched product $(a\bullet b\bullet c)\times I$ of $\cC$.
\begin{figure}[t]
$$
\mathfig{0.4}{triangle/triangle4a}
$$
-\nn{remember to change the labels}
+$$
+\begin{tikzpicture}
+\node[circle,fill=black,inner sep=1pt] at (1.73,0) {};
+\node[circle,fill=black,inner sep=1pt] at (-1.73,0) {};
+\begin{scope}[yshift=-1cm]
+\path[clip] (0,0) circle (2);
+\begin{scope}[yshift=2cm]
+\draw (0,0) circle (2);
+\node[circle,fill=black,inner sep=1pt] (L2) at (-90:2) {};
+\node[circle,fill=black,inner sep=1pt] (L1) at (-120:2) {};
+\node at (-60:2.25) {$c$};
+\node at (-105:2.25) {$b$};
+\node at (-135:2.25) {$a$};
+\end{scope}
+\end{scope}
+\begin{scope}[yshift=1cm]
+\path[clip] (0,0) circle (2);
+\begin{scope}[yshift=-2cm]
+\node at (120:2.25) {$a$};
+\node at (75:2.25) {$b$};
+\node at (45:2.25) {$c$};
+\draw (0,0) circle (2);
+\node[circle,fill=black,inner sep=1pt] (U1) at (90:2) {};
+\node[circle,fill=black,inner sep=1pt] (U2) at (60:2) {};
+\end{scope}
+\end{scope}
+\draw[dashed] (L1) -- (U1);
+\draw[dashed] (L2) -- (U2);
+\begin{scope}
+\path[clip] (0,1) circle (2);
+\path[clip] (0,-1) circle (2);
+ \foreach \t in {-2.5,-2.4,...,-1.2} {
+ \draw[green!50!brown] (\t,-1) -- +(1.19,2);
+ }
+ \foreach \t in {-1.1,-1.0,...,0} {
+ \draw[blue!50!brown] (\t,-1) -- +(1.19,2);
+ }
+ \foreach \t in {0.1,0.2,...,2.5} {
+ \draw[red!50!brown] (\t,-1) -- +(1.19,2);
+ }
+\end{scope}
+\draw[->, thick, blue!75!yellow] (-2,0.5) node[black, left] {$a\times I$} -- (-1,0.5);
+\draw[->, thick, blue!75!yellow] (-0.25,-1.5) node[black, below] {$b\times I$} -- (-0.25,-0.5);
+\draw[->, thick, blue!75!yellow] (2,-0.5) node[black, right] {$c\times I$} -- (1,-0.5);
+\end{tikzpicture}
+$$
\caption{An associator.}
\label{fig:associator}
\end{figure}