
diff -r 19e58f33cdc3 -r 96ec10a46ee1 text/ncat.tex
--- 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.




