--- a/text/appendixes/comparing_defs.tex	Fri Aug 12 10:00:59 2011 -0600
+++ b/text/appendixes/comparing_defs.tex	Sun Sep 25 14:44:38 2011 -0600
@@ -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 $\cC(I; x, y)$
@@ -622,7 +622,7 @@
 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.