--- a/text/appendixes/comparing_defs.tex	Tue Aug 09 23:55:13 2011 -0700
+++ b/text/appendixes/comparing_defs.tex	Sun Sep 25 14:33:30 2011 -0600
@@ -4,8 +4,8 @@
 \label{sec:comparing-defs}
 
 In \S\ref{sec:example:traditional-n-categories(fields)} we showed how to construct
-a disk-like  $n$-category from a traditional $n$-category; the morphisms of the 
-disk-like  $n$-category are string diagrams labeled by the traditional $n$-category.
+a topological $n$-category from a traditional $n$-category; the morphisms of the 
+topological $n$-category are string diagrams labeled by the traditional $n$-category.
 In this appendix we sketch how to go the other direction, for $n=1$ and 2.
 The basic recipe, given a disk-like $n$-category $\cC$, is to define the $k$-morphisms
 of the corresponding traditional $n$-category to be $\cC(B^k)$, where
@@ -575,11 +575,11 @@
 \subsection{\texorpdfstring{$A_\infty$}{A-infinity} 1-categories}
 \label{sec:comparing-A-infty}
 In this section, we make contact between the usual definition of an $A_\infty$ category 
-and our definition of an $A_\infty$ disk-like $1$-category, from \S \ref{ss:n-cat-def}.
+and our definition of a disk-like $A_\infty$ $1$-category, from \S \ref{ss:n-cat-def}.
 
 \medskip
 
-Given an $A_\infty$ disk-like $1$-category $\cC$, we define an ``$m_k$-style" 
+Given a disk-like $A_\infty$ $1$-category $\cC$, we define an ``$m_k$-style" 
 $A_\infty$ $1$-category $A$ as follows.
 The objects of $A$ are $\cC(pt)$.
 The morphisms of $A$, from $x$ to $y$, are $\cC(I; x, y)$
@@ -621,7 +621,7 @@
 Operad associativity for $A$ implies that this gluing map is independent of the choice of
 $g$ and the choice of representative $(f_i, a_i)$.
 
-It is straightforward to verify the remaining axioms for a $A_\infty$ disk-like 1-category.
+It is straightforward to verify the remaining axioms for a disk-like $A_\infty$ 1-category.