--- a/text/intro.tex	Mon Aug 30 13:19:05 2010 -0700
+++ b/text/intro.tex	Tue Aug 31 11:18:26 2010 -0700
@@ -76,9 +76,9 @@
 
 In \S \ref{ss:ncat_fields}  we explain how to construct a system of fields from a topological $n$-category 
 (using a colimit along certain decompositions of a manifold into balls). 
-With this in hand, we freely write $\bc_*(M; \cC)$ to indicate the blob complex of a manifold $M$ 
+With this in hand, we write $\bc_*(M; \cC)$ to indicate the blob complex of a manifold $M$ 
 with the system of fields constructed from the $n$-category $\cC$. 
-\nn{KW: I don't think we use this notational convention any more, right?}
+%\nn{KW: I don't think we use this notational convention any more, right?}
 In \S \ref{sec:ainfblob} we give an alternative definition 
 of the blob complex for an $A_\infty$ $n$-category on an $n$-manifold (analogously, using a homotopy colimit).
 Using these definitions, we show how to use the blob complex to ``resolve" any topological $n$-category as an 
@@ -127,7 +127,7 @@
 \draw[->] (BC) -- node[left] {$H_0$} node[right] {c.f. Theorem \ref{thm:skein-modules}} (A);
 
 \draw[->] (FU) -- node[left] {blob complex \\ for balls} (Cs);
-\draw (BC) -- node[right] {$\iso$ by \\ Corollary \ref{cor:new-old}} (BCs);
+\draw[<->] (BC) -- node[right] {$\iso$ by \\ Corollary \ref{cor:new-old}} (BCs);
 \end{tikzpicture}
 
 }
@@ -139,8 +139,8 @@
 Section \S \ref{sec:deligne} gives
 a higher dimensional generalization of the Deligne conjecture 
 (that the little discs operad acts on Hochschild cochains) in terms of the blob complex.
-The appendixes prove technical results about $\CH{M}$ and the ``small blob complex", 
-and make connections between our definitions of $n$-categories and familiar definitions for $n=1$ and $n=2$, 
+The appendices prove technical results about $\CH{M}$ and
+make connections between our definitions of $n$-categories and familiar definitions for $n=1$ and $n=2$, 
 as well as relating the $n=1$ case of our $A_\infty$ $n$-categories with usual $A_\infty$ algebras. 
 Appendix \ref{sec:comm_alg} describes the blob complex when $\cC$ is a commutative algebra, 
 thought of as a topological $n$-category, in terms of the topology of $M$.
@@ -343,9 +343,9 @@
 }
 \end{equation*}
 \end{enumerate}
-Moreover any such chain map is unique, up to an iterated homotopy.
-(That is, any pair of homotopies have a homotopy between them, and so on.)
-\nn{revisit this after proof below has stabilized}
+%Moreover any such chain map is unique, up to an iterated homotopy.
+%(That is, any pair of homotopies have a homotopy between them, and so on.)
+%\nn{revisit this after proof below has stabilized}
 \end{thm:CH}
 
 \newtheorem*{thm:CH-associativity}{Theorem \ref{thm:CH-associativity}}

--- a/text/ncat.tex	Mon Aug 30 13:19:05 2010 -0700
+++ b/text/ncat.tex	Tue Aug 31 11:18:26 2010 -0700
@@ -17,14 +17,14 @@
 The definitions presented below tie the categories more closely to the topology
 and avoid combinatorial questions about, for example, the minimal sufficient
 collections of generalized associativity axioms; we prefer maximal sets of axioms to minimal sets.
-For examples of topological origin
+It is easy to show that examples of topological origin
 (e.g.\ categories whose morphisms are maps into spaces or decorated balls), 
-it is easy to show that they
 satisfy our axioms.
 For examples of a more purely algebraic origin, one would typically need the combinatorial
 results that we have avoided here.
 
-\nn{Say something explicit about Lurie's work here? It seems like this was something that Dan Freed wanted explaining when we talked to him in Aspen}
+%\nn{Say something explicit about Lurie's work here? 
+%It seems like this was something that Dan Freed wanted explaining when we talked to him in Aspen}
 
 \medskip
 
@@ -190,7 +190,8 @@
 \caption{Combining two balls to get a full boundary.}\label{blah3}\end{figure}
 
 Note that we insist on injectivity above. 
-The lemma follows from Definition \ref{def:colim-fields} and Lemma \ref{lem:colim-injective}. \nn{we might want a more official looking proof...}
+The lemma follows from Definition \ref{def:colim-fields} and Lemma \ref{lem:colim-injective}.
+%\nn{we might want a more official looking proof...}
 
 Let $\cl{\cC}(S)_E$ denote the image of $\gl_E$.
 We will refer to elements of $\cl{\cC}(S)_E$ as ``splittable along $E$" or ``transverse to $E$". 
@@ -890,12 +891,12 @@
 The remaining data for the $A_\infty$ $n$-category 
 --- composition and $\Diff(X\to X')$ action ---
 also comes from the $\cE\cB_n$ action on $A$.
-\nn{should we spell this out?}
+%\nn{should we spell this out?}
 
 Conversely, one can show that a topological $A_\infty$ $n$-category $\cC$, where the $k$-morphisms
 $\cC(X)$ are trivial (single point) for $k<n$, gives rise to 
 an $\cE\cB_n$-algebra.
-\nn{The paper is already long; is it worth giving details here?}
+%\nn{The paper is already long; is it worth giving details here?}
 
 If we apply the homotopy colimit construction of the next subsection to this example, 
 we get an instance of Lurie's topological chiral homology construction.