
diff -r 1fc5fff34251 -r 76a569bb2cec text/ncat.tex
--- a/text/ncat.tex	Fri Aug 05 12:02:42 2011 -0600
+++ b/text/ncat.tex	Fri Aug 05 12:23:45 2011 -0600
@@ -2371,6 +2371,10 @@
 The only requirement is that each $k$-sphere module be a module for a $k$-sphere $n{-}k$-category
 constructed out of labels taken from $L_j$ for $j<k$.
 
+We remind the reader again that $\cS = \cS_{\{L_i\}, \{z_Y\}}$ depends on 
+the choice of $L_i$ above as well as the choice of 
+families of inner products below.
+
 We now define $\cS(X)$, for $X$ a ball of dimension at most $n$, to be the set of all 
 cell-complexes $K$ embedded in $X$, with the codimension-$j$ parts of $(X, K)$ labeled
 by elements of $L_j$.
@@ -2396,7 +2400,7 @@
 
 Let $X$ be an $n{+}1$-ball, and let $c$ be a decoration of its boundary
 by a cell complex labeled by 0- through $n$-morphisms, as above.
-Choose an $n{-}1$-sphere $E\sub \bd X$ which divides
+Choose an $n{-}1$-sphere $E\sub \bd X$, transverse to $c$, which divides
 $\bd X$ into ``incoming" and ``outgoing" boundary $\bd_-X$ and $\bd_+X$.
 Let $E_c$ denote $E$ decorated by the restriction of $c$ to $E$.
 Recall from above the associated 1-category $\cS(E_c)$.




