--- a/text/appendixes/famodiff.tex	Tue Jun 28 15:43:53 2011 -0700
+++ b/text/appendixes/famodiff.tex	Tue Jun 28 15:44:04 2011 -0700
@@ -29,9 +29,9 @@
 \[
 	F: I \times P\times X \to T
 \]
-such that
+such that the following conditions hold.
 \begin{enumerate}
-\item $F(0, \cdot, \cdot) = f$ .
+\item $F(0, \cdot, \cdot) = f$.
 \item We can decompose $P = \cup_i D_i$ so that
 the restrictions $F(1, \cdot, \cdot) : D_i\times X\to T$ are all adapted to $\cU$.
 \item If $f$ has support $S\sub X$, then

--- a/text/ncat.tex	Tue Jun 28 15:43:53 2011 -0700
+++ b/text/ncat.tex	Tue Jun 28 15:44:04 2011 -0700
@@ -1521,12 +1521,6 @@
 $\cl{\cC}(W)$ is functorial with respect to homeomorphisms of $k$-manifolds. 
 Restricting the $k$-spheres, we have now proved Lemma \ref{lem:spheres}.
 
-It is easy to see that
-there are well-defined maps $\cl{\cC}(W)\to\cl{\cC}(\bd W)$, and that these maps
-comprise a natural transformation of functors.
-
-
-
 \begin{lem}
 \label{lem:colim-injective}
 Let $W$ be a manifold of dimension less than $n$.  Then for each