
diff -r 1e4bb652812d -r 3e1d7e7f8dfd text/ncat.tex
--- a/text/ncat.tex	Sat Jul 16 11:39:58 2011 -0600
+++ b/text/ncat.tex	Sat Jul 16 12:22:23 2011 -0600
@@ -2578,10 +2578,10 @@
 
 It follows from the lemma that we can construct an isomorphism
 between $\cS(X; c; E)$ and $\cS(X; c; E')$ for any pair $E$, $E'$.
-This construction involves on a choice of simple ``moves" (as above) to transform
+This construction involves a choice of simple ``moves" (as above) to transform
 $E$ to $E'$.
 We must now show that the isomorphism does not depend on this choice.
-We will show below that it suffice to check two ``movie moves".
+We will show below that it suffices to check two ``movie moves".
 
 The first movie move is to push $E$ across an $n$-ball $B$ as above, then push it back.
 The result is equivalent to doing nothing.
@@ -2675,7 +2675,7 @@
 %The third movie move could be called ``locality" or ``disjoint commutativity".
 %\nn{...}
 
-If $n\ge 2$, these two movie move suffice:
+If $n\ge 2$, these two movie moves suffice:
 
 \begin{lem}
 Assume $n\ge 2$ and fix $E$ and $E'$ as above.
@@ -2696,7 +2696,7 @@
 (This fails for $n=1$.)
 \end{proof}
 
-For $n=1$ we have to check an additional ``global" relations corresponding to 
+For $n=1$ we have to check an additional ``global" relation corresponding to 
 rotating the 0-sphere $E$ around the 1-sphere $\bd X$.
 But if $n=1$, then we are in the case of ordinary algebroids and bimodules,
 and this is just the well-known ``Frobenius reciprocity" result for bimodules \cite{MR1424954}.




