# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1283373261 25200
# Node ID b236746e8e4daad5f351fd81d8c81869d1c4a51f
# Parent  8e055b7c0768f2d5a2f76e7589e3b309ec18ea91
futzing with figures (\begin{center|equation} to \centering)

diff -r 8e055b7c0768 -r b236746e8e4d text/a_inf_blob.tex
--- a/text/a_inf_blob.tex	Tue Aug 31 21:09:31 2010 -0700
+++ b/text/a_inf_blob.tex	Wed Sep 01 13:34:21 2010 -0700
@@ -113,8 +113,7 @@
 give the desired chain connecting $(a, K)$ and $(a, K')$
 (see Figure \ref{zzz4}).
 
-\begin{figure}[!ht]
-\begin{equation*}
+\begin{figure}[t] \centering
 \begin{tikzpicture}
 \foreach \x/\label in {-3/K, 0/L, 3/K'} {
 	\node(\label) at (\x,0) {$\label$};
@@ -125,7 +124,6 @@
 	\draw[->] (\la \lb) -- (\lb); 
 }
 \end{tikzpicture}
-\end{equation*}
 \caption{Connecting $K$ and $K'$ via $L$}
 \label{zzz4}
 \end{figure}
@@ -139,11 +137,7 @@
 Then we have 2-simplices, as shown in Figure \ref{zzz5}, which do the trick.
 (Each small triangle in Figure \ref{zzz5} can be filled with a 2-simplex.)
 
-\begin{figure}[!ht]
-%\begin{equation*}
-%\mathfig{1.0}{tempkw/zz5}
-%\end{equation*}
-\begin{equation*}
+\begin{figure}[t] \centering
 \begin{tikzpicture}
 \node(M) at (0,0) {$M$};
 \foreach \angle/\label in {0/K', 45/K'L, 90/L, 135/KL, 180/K, 225/KL', 270/L', 315/K'L'} {
@@ -174,7 +168,6 @@
 \draw[->] (KL) to[bend right=10] (K);
 \draw[->] (KL) to[bend left=10] (L);
 \end{tikzpicture}
-\end{equation*}
 \caption{Filling in $K$-$KL$-$L$-$K'L$-$K'$-$K'L'$-$L'$-$KL'$-$K$}
 \label{zzz5}
 \end{figure}
diff -r 8e055b7c0768 -r b236746e8e4d text/appendixes/comparing_defs.tex
--- 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}
diff -r 8e055b7c0768 -r b236746e8e4d text/ncat.tex
--- a/text/ncat.tex	Tue Aug 31 21:09:31 2010 -0700
+++ b/text/ncat.tex	Wed Sep 01 13:34:21 2010 -0700
@@ -1639,7 +1639,7 @@
 More specifically, $D\to D'$ is an antirefinement if $D'$ is obtained from $D$ by 
 gluing subintervals together and/or omitting some of the rightmost subintervals.
 (See Figure \ref{fig:lmar}.)
-\begin{figure}[t]$$
+\begin{figure}[t] \centering
 \definecolor{arcolor}{rgb}{.75,.4,.1}
 \begin{tikzpicture}[line width=1pt]
 \fill (0,0) circle (.1);
@@ -1679,7 +1679,6 @@
 }
 
 \end{tikzpicture}
-$$
 \caption{Antirefinements of left-marked intervals}\label{fig:lmar}\end{figure}
 
 Now we define the chain complex $\hom_\cC(\cX_\cC \to \cY_\cC)$.
@@ -1735,7 +1734,7 @@
 These are required to commute with gluing;
 for each subdivision $K = I_1\cup\cdots\cup I_q$ the following diagram commutes:
 \[ \xymatrix{
-	\cX(I_1)\ot\cC(I_2)\ot\cdots\ot\cC(I_q) \ar[r]^{h_{I_0}\ot \id} 
+	\cX(I_1)\ot\cC(I_2)\ot\cdots\ot\cC(I_q) \ar[r]^{h_{I_1}\ot \id} 
 							\ar[d]_{\gl} & \cY(I_1)\ot\cC(I_2)\ot\cdots\ot\cC(I_q) 
 								\ar[d]^{\gl} \\
 	\cX(K) \ar[r]^{h_{K}} & \cY(K)
@@ -1875,8 +1874,7 @@
 (see Figure \ref{feb21b}).
 These restrictions are 0-morphisms $(a, b)$ of $\cA$ and $\cB$.
 
-\begin{figure}[t]
-$$
+\begin{figure}[t] \centering
 \begin{tikzpicture}[blue,line width=2pt]
 \draw (0,1) -- (0,-1) node[below] {$X$};
 
@@ -1891,7 +1889,6 @@
 \path (bottom) node[below]{$X \times J$};
 
 \end{tikzpicture}
-$$
 \caption{The pinched product $X\times J$}
 \label{feb21b}
 \end{figure}
@@ -1904,8 +1901,7 @@
 to obtain an $\cA_0$-$\cA_l$ $0$-sphere module and, forgetfully, an $n{-}1$-category.
 This amounts to a definition of taking tensor products of $0$-sphere modules over $n$-categories.
 
-\begin{figure}[t]
-$$
+\begin{figure}[t] \centering
 \begin{tikzpicture}[baseline,line width = 2pt]
 \draw[blue] (0,0) -- (6,0);
 \foreach \x/\n in {0.5/0,1.5/1,3/2,4.5/3,5.5/4} {
@@ -1927,7 +1923,6 @@
 	\path (\q:2.4) node {\color{green!50!brown}$\cM_{\n}$};
 }
 \end{tikzpicture}
-$$
 \caption{Marked and labeled 1-manifolds}
 \label{feb21c}
 \end{figure}
@@ -1956,8 +1951,7 @@
 (See Figure \nn{need figure}.)
 We now proceed as in the above module definitions.
 
-\begin{figure}[!ht]
-$$
+\begin{figure}[t] \centering
 \begin{tikzpicture}[baseline,line width = 2pt]
 \draw[blue][fill=blue!15!white] (0,0) circle (2);
 \fill[red] (0,0) circle (0.1);
@@ -1968,7 +1962,6 @@
 	\draw[line width=1pt, green!50!brown, ->] (M\n.\qm+135) to[out=\qm+135,in=\qm+90] (\qm+5:1.3);
 }
 \end{tikzpicture}
-$$
 \caption{Cone on a marked circle}
 \label{feb21d}
 \end{figure}