--- 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}
--- 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}
--- 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}