# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1313164859 21600
# Node ID ab0b4827c89c43dec926f8e4d3fc3a6bf12f4fa5
# Parent  c570a7a75b07da7aa123d9b94449eb2f7c5a2149
more referee report stuff, relatively minor

diff -r c570a7a75b07 -r ab0b4827c89c RefereeReport.pdf
Binary file RefereeReport.pdf has changed
diff -r c570a7a75b07 -r ab0b4827c89c text/appendixes/comparing_defs.tex
--- a/text/appendixes/comparing_defs.tex	Thu Aug 11 22:14:11 2011 -0600
+++ b/text/appendixes/comparing_defs.tex	Fri Aug 12 10:00:59 2011 -0600
@@ -585,6 +585,7 @@
 The morphisms of $A$, from $x$ to $y$, are $\cC(I; x, y)$
 ($\cC$ applied to the standard interval with boundary labeled by $x$ and $y$).
 For simplicity we will now assume there is only one object and suppress it from the notation.
+Henceforth $A$ will also denote its unique morphism space.
 
 A choice of homeomorphism $I\cup I \to I$ induces a chain map $m_2: A\otimes A\to A$.
 We now have two different homeomorphisms $I\cup I\cup I \to I$, but they are isotopic.
@@ -610,7 +611,7 @@
 We define a $\Homeo(J)$ action on $\cC(J)$ via $g_*(f, a) = (g\circ f, a)$.
 The $C_*(\Homeo(J))$ action is defined similarly.
 
-Let $J_1$ and $J_2$ be intervals.
+Let $J_1$ and $J_2$ be intervals, and let $J_1\cup J_2$ denote their union along a single boundary point.
 We must define a map $\cC(J_1)\ot\cC(J_2)\to\cC(J_1\cup J_2)$.
 Choose a homeomorphism $g:I\to J_1\cup J_2$.
 Let $(f_i, a_i)\in \cC(J_i)$.
diff -r c570a7a75b07 -r ab0b4827c89c text/intro.tex
--- a/text/intro.tex	Thu Aug 11 22:14:11 2011 -0600
+++ b/text/intro.tex	Fri Aug 12 10:00:59 2011 -0600
@@ -260,8 +260,7 @@
 Note that this includes the case of gluing two disjoint manifolds together.
 \begin{property}[Gluing map]
 \label{property:gluing-map}%
-Given a gluing $X \to X_\mathrm{gl}$, there is
-a natural map
+Given a gluing $X \to X_\mathrm{gl}$, there is an injective natural map
 \[
 	\bc_*(X) \to \bc_*(X_\mathrm{gl}) 
 \]
diff -r c570a7a75b07 -r ab0b4827c89c text/ncat.tex
--- a/text/ncat.tex	Thu Aug 11 22:14:11 2011 -0600
+++ b/text/ncat.tex	Fri Aug 12 10:00:59 2011 -0600
@@ -1001,6 +1001,8 @@
 
 In the $n$-category axioms above we have intermingled data and properties for expository reasons.
 Here's a summary of the definition which segregates the data from the properties.
+We also remind the reader of the inductive nature of the definition: All the data for $k{-}1$-morphisms must be in place
+before we can describe the data for $k$-morphisms.
 
 A disk-like $n$-category consists of the following data:
 \begin{itemize}
diff -r c570a7a75b07 -r ab0b4827c89c text/tqftreview.tex
--- a/text/tqftreview.tex	Thu Aug 11 22:14:11 2011 -0600
+++ b/text/tqftreview.tex	Fri Aug 12 10:00:59 2011 -0600
@@ -89,9 +89,11 @@
 then this extra structure is considered part of the definition of $\cC_n$.
 Any maps mentioned below between fields on $n$-manifolds must be morphisms in $\cS$.
 \item $\cC_k$ is compatible with the symmetric monoidal
-structures on $\cM_k$, $\Set$ and $\cS$: $\cC_k(X \du W) \cong \cC_k(X)\times \cC_k(W)$,
+structures on $\cM_k$, $\Set$ and $\cS$.
+For $k<n$ we have $\cC_k(X \du W) \cong \cC_k(X)\times \cC_k(W)$,
 compatibly with homeomorphisms and restriction to boundary.
-We will call the projections $\cC(X_1 \du X_2) \to \cC(X_i)$
+For $k=n$ we require $\cC_n(X \du W; c\du d) \cong \cC_k(X, c)\ot \cC_k(W, d)$.
+We will call the projections $\cC_k(X_1 \du X_2) \to \cC_k(X_i)$
 restriction maps.
 \item Gluing without corners.
 Let $\bd X = Y \du Y \du W$, where $Y$ and $W$ are closed $k{-}1$-manifolds.