# HG changeset patch
# User Scott Morrison <scott@tqft.net>
# Date 1280341601 25200
# Node ID 045e01f63729845d2b2367be71c5bd977afd1b65
# Parent  e9ef2270eb6106e1ace53d25e5e7cf24a83a3af3
minor

diff -r e9ef2270eb61 -r 045e01f63729 text/blobdef.tex
--- a/text/blobdef.tex	Wed Jul 28 11:20:28 2010 -0700
+++ b/text/blobdef.tex	Wed Jul 28 11:26:41 2010 -0700
@@ -67,7 +67,7 @@
 just erasing the blob from the picture
 (but keeping the blob label $u$).
 
-\nn{it seems rather strange to make this a theorem}
+\nn{it seems rather strange to make this a theorem} \nn{it's a theorem because it's stated in the introduction, and I wanted everything there to have numbers that pointed into the paper --S}
 Note that directly from the definition we have
 \begin{thm}
 \label{thm:skein-modules}
@@ -151,7 +151,7 @@
 (This is necessary for Proposition \ref{blob-gluing}.)
 \end{itemize}
 Combining these two operations can give rise to configurations of blobs whose complement in $X$ is not
-a manifold. \todo{example}
+a manifold.
 Thus will need to be more careful when speaking of a field $r$ on the complement of the blobs.
 
 \begin{example}
@@ -240,8 +240,8 @@
 \end{itemize}
 For example, a diagram of $k$ strictly nested blobs corresponds to a $k$-simplex, while
 a diagram of $k$ disjoint blobs corresponds to a $k$-cube.
-(This correspondence works best if we think of each twig label $u_i$ as having the form
+(When the fields come from an $n$-category, this correspondence works best if we think of each twig label $u_i$ as having the form
 $x - s(e(x))$, where $x$ is an arbitrary field on $B_i$, $e: \cF(B_i) \to C$ is the evaluation map, 
-and $s:C \to \cF(B_i)$ is some fixed section of $e$. \todo{This parenthetical remark mysteriously specialises to the category case})
+and $s:C \to \cF(B_i)$ is some fixed section of $e$.)
 
 
diff -r e9ef2270eb61 -r 045e01f63729 text/intro.tex
--- a/text/intro.tex	Wed Jul 28 11:20:28 2010 -0700
+++ b/text/intro.tex	Wed Jul 28 11:26:41 2010 -0700
@@ -97,7 +97,7 @@
 \node[box] at (-4,\yb) (tC) {$C$ \\ a `traditional' \\ weak $n$-category};
 \node[box] at (\xa,\ya) (C) {$\cC$ \\ a topological \\ $n$-category};
 \node[box] at (\xb,\ya) (A) {$\underrightarrow{\cC}(M)$ \\ the (dual) TQFT \\ Hilbert space};
-\node[box] at (\xa,\yb) (FU) {$(\cF, \cU)$ \\ fields and\\ local relations};
+\node[box] at (\xa,\yb) (FU) {$(\cF, U)$ \\ fields and\\ local relations};
 \node[box] at (\xb,\yb) (BC) {$\bc_*(M; \cF)$ \\ the blob complex};
 \node[box] at (\xa,\yc) (Cs) {$\cC_*$ \\ an $A_\infty$ \\$n$-category};
 \node[box] at (\xb,\yc) (BCs) {$\underrightarrow{\cC_*}(M)$};
@@ -108,13 +108,13 @@
 \draw[->] (FU) -- node[below] {blob complex \\ for $M$} (BC);
 \draw[->] (Cs) -- node[above] {$\displaystyle \hocolim_{\cell(M)} \cC_*$} node[below] {\S \ref{ss:ncat_fields}} (BCs);
 
-\draw[->] (FU) -- node[right=10pt] {$\cF(M)/\cU$} (A);
+\draw[->] (FU) -- node[right=10pt] {$\cF(M)/U$} (A);
 
 \draw[->] (tC) -- node[above] {Example \ref{ex:traditional-n-categories(fields)}} (FU);
 
 \draw[->] (C.-100) -- node[left] {
 	\S \ref{ss:ncat_fields}
-	%$\displaystyle \cF(M) = \DirectSum_{c \in\cell(M)} \cC(c)$ \\ $\displaystyle \cU(B) = \DirectSum_{c \in \cell(B)} \ker \ev: \cC(c) \to \cC(B)$
+	%$\displaystyle \cF(M) = \DirectSum_{c \in\cell(M)} \cC(c)$ \\ $\displaystyle U(B) = \DirectSum_{c \in \cell(B)} \ker \ev: \cC(c) \to \cC(B)$
    } (FU.100);
 \draw[->] (C) -- node[above left=3pt] {restrict to \\ standard balls} (tC);
 \draw[->] (FU.80) -- node[right] {restrict \\ to balls} (C.-80);