
diff -r eec1fd45225a -r 858b80dfa05c text/ncat.tex
--- a/text/ncat.tex	Wed Jun 22 16:02:37 2011 -0700
+++ b/text/ncat.tex	Wed Jun 22 16:07:55 2011 -0700
@@ -1980,13 +1980,13 @@
 
 In this subsection we define $n{+}1$-categories $\cS$ of ``sphere modules".
 The objects are $n$-categories, the $k$-morphisms are $k{-}1$-sphere modules for $1\le k \le n$,
-and the $n{+}1$-morphisms are intertwinors.
+and the $n{+}1$-morphisms are intertwiners.
 With future applications in mind, we treat simultaneously the big category
 of all $n$-categories and all sphere modules and also subcategories thereof.
 When $n=1$ this is closely related to familiar $2$-categories consisting of 
 algebras, bimodules and intertwiners (or a subcategory of that).
 The sphere module $n{+}1$-category is a natural generalization of the 
-algebra-bimodule-intertwinor 2-category to higher dimensions.
+algebra-bimodule-intertwiner 2-category to higher dimensions.
 
 Another possible name for this $n{+}1$-category is $n{+}1$-category of defects.
 The $n$-categories are thought of as representing field theories, and the 
@@ -2594,7 +2594,7 @@
 
 We end this subsection with some remarks about Morita equivalence of disklike $n$-categories.
 Recall that two 1-categories $\cC$ and $\cD$ are Morita equivalent if and only if they are equivalent
-objects in the 2-category of (linear) 1-categories, bimodules, and intertwinors.
+objects in the 2-category of (linear) 1-categories, bimodules, and intertwiners.
 Similarly, we define two disklike $n$-categories to be Morita equivalent if they are equivalent objects in the
 $n{+}1$-category of sphere modules.
 
@@ -2624,14 +2624,14 @@
 
 We want the 2-morphisms from the previous paragraph to be equivalences, so we need 3-morphisms
 between various compositions of these 2-morphisms and various identity 2-morphisms.
-Recall that the 3-morphisms of $\cS$ are intertwinors between representations of 1-categories associated
+Recall that the 3-morphisms of $\cS$ are intertwiners between representations of 1-categories associated
 to decorated circles.
 Figure \ref{morita-fig-2} 
 \begin{figure}[t]
 $$\mathfig{.55}{tempkw/morita2}$$
-\caption{Intertwinors for a Morita equivalence}\label{morita-fig-2}
+\caption{intertwiners for a Morita equivalence}\label{morita-fig-2}
 \end{figure}
-shows the intertwinors we need.
+shows the intertwiners we need.
 Each decorated 2-ball in that figure determines a representation of the 1-category associated to the decorated circle
 on the boundary.
 This is the 3-dimensional part of the data for the Morita equivalence.
@@ -2644,15 +2644,15 @@
 These are illustrated in Figure \ref{morita-fig-3}.
 \begin{figure}[t]
 $$\mathfig{.65}{tempkw/morita3}$$
-\caption{Identities for intertwinors}\label{morita-fig-3}
+\caption{Identities for intertwiners}\label{morita-fig-3}
 \end{figure}
-Each line shows a composition of two intertwinors which we require to be equal to the identity intertwinor.
+Each line shows a composition of two intertwiners which we require to be equal to the identity intertwiner.
 
 For general $n$, we start with an $n$-category 0-sphere module $\cM$ which is the data for the 1-dimensional
 part of the Morita equivalence.
 For $2\le k \le n$, the $k$-dimensional parts of the Morita equivalence are various decorated $k$-balls with submanifolds
 labeled by $\cC$, $\cD$ and $\cM$; no additional data is needed for these parts.
-The $n{+}1$-dimensional part of the equivalence is given by certain intertwinors, and these intertwinors must 
+The $n{+}1$-dimensional part of the equivalence is given by certain intertwiners, and these intertwiners must 
 be invertible and satisfy
 identities corresponding to Morse cancellations in $n$-manifolds. 
 




