--- a/text/appendixes/comparing_defs.tex	Tue Aug 31 21:09:31 2010 -0700
+++ b/text/appendixes/comparing_defs.tex	Wed Sep 01 13:34:21 2010 -0700
@@ -137,7 +137,7 @@
 We will define a ``horizontal" composition later.
 
 \begin{figure}[t]
-\begin{center}
+\centering
 \begin{tikzpicture}
 
 \newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}}
@@ -183,7 +183,6 @@
 \draw[->, thick, blue!50!green] (A) -- node[black, above] {$\cong$} (B);
 
 \end{tikzpicture}
-\end{center}
 \caption{Vertical composition of 2-morphisms}
 \label{fzo1}
 \end{figure}
@@ -204,7 +203,7 @@
 Define 2-morphsims $a \to a\bullet \id_x$ and $a\bullet \id_x \to a$
 as shown in Figure \ref{fzo2}.
 \begin{figure}[t]
-\begin{center}
+\centering
 \begin{tikzpicture}
 \newcommand{\rr}{6}
 \newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}}
@@ -274,7 +273,6 @@
 \draw[->] (A) -- (B);
 \draw[->] (A) -- (C);
 \end{tikzpicture}
-\end{center}
 \caption{Producing weak identities from half pinched products}
 \label{fzo2}
 \end{figure}
@@ -284,7 +282,7 @@
 on $a$ and $a\bullet \id_x$, as defined above.
 Figure \ref{fzo3} shows one case.
 \begin{figure}[t]
-\begin{center}
+\centering
 \begin{tikzpicture}
 
 \newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}}
@@ -400,14 +398,13 @@
 \draw[->, thick, blue!50!green] (B) -- node[black, above] {$=$} (C);
 
 \end{tikzpicture}
-\end{center}
 \caption{Composition of weak identities, 1}
 \label{fzo3}
 \end{figure}
 In the first step we have inserted a copy of $(x\times I)\times I$.
 Figure \ref{fzo4} shows the other case.
 \begin{figure}[t]
-\begin{center}
+\centering
 \begin{tikzpicture}
 
 \newcommand{\vertex}{node[circle,fill=black,inner sep=1pt] {}}
@@ -502,7 +499,6 @@
 \draw[->, thick, blue!50!green] ($(B) + (1,0)$) -- node[black, above] {$=$} (C);
 
 \end{tikzpicture}
-\end{center}
 \caption{Composition of weak identities, 2}
 \label{fzo4}
 \end{figure}