--- a/pnas/pnas.tex	Mon Nov 15 08:15:28 2010 -0800
+++ b/pnas/pnas.tex	Tue Nov 16 16:55:49 2010 -0800
@@ -158,6 +158,12 @@
 %% \subsection{}
 %% \subsubsection{}
 
+\dropcap{T}he aim of this paper is to describe a derived category version of TQFTs.
+
+For our purposes, an $n{+}1$-dimensional TQFT is a locally defined system of
+invariants of manifolds of dimensions 0 through $n+1$.
+
+
 \dropcap{T}opological quantum field theories (TQFTs) provide local invariants of manifolds, which are determined by the algebraic data of a higher category.
 
 An $n+1$-dimensional TQFT $\cA$ associates a vector space $\cA(M)$