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 More specifically, life is easier when working with maximal, rather than minimal, collections of axioms.}
 \nn{say something about defining plain and infty cases simultaneously}
 There are five basic ingredients
-(not two, or four, or seven, but {\bf five} basic ingredients,
+\cite{life-of-brian} of an $n$-category definition:
-which he shall wield all wretched sinners and that includes on you, sir, there in the front row!
-(cf.\ Monty Python, Life of Brian, http://www.youtube.com/watch?v=fIRb8TigJ28))
-of an $n$-category definition:
 $k$-morphisms (for $0\le k \le n$), domain and range, composition,
 identity morphisms, and special behavior in dimension $n$ (e.g. enrichment
 in some auxiliary category, or strict associativity instead of weak associativity).
 We will treat each of these in turn.
 \end{proof}
 \subsection{Specializations}
 \label{sec:specializations}
-The blob complex has two important special cases.
+The blob complex has several important special cases.
 \begin{thm}[Skein modules]
 \label{thm:skein-modules}
 \nn{Plain n-categories only?}
 The $0$-th blob homology of $X$ is the usual
 Theorem \ref{thm:skein-modules} is immediate from the definition, and
 Theorem \ref{thm:hochschild} is established by extending the statement to bimodules as well as categories, then verifying that the universal properties of Hochschild homology also hold for $\bc_*(S^1; -)$.
+\begin{thm}[Mapping spaces]
+\label{thm:map-recon}
+Let $\pi^\infty_{\le n}(T)$ denote the $A_\infty$ $n$-category based on maps
+$B^n \to T$.
+(The case $n=1$ is the usual $A_\infty$-category of paths in $T$.)
+Then
+$$\bc_*(X; \pi^\infty_{\le n}(T)) \simeq \CM{X}{T}.$$
+\end{thm}
+This says that we can recover (up to homotopy) the space of maps to $T$ via blob homology from local data.
+Note that there is no restriction on the connectivity of $T$ as there is for the corresponding result in topological chiral homology \cite[Theorem 3.8.6]{0911.0018}.
+\todo{sketch proof}
 \subsection{Structure of the blob complex}
 \label{sec:structure}
 In the following $\CH{X} = C_*(\Homeo(X))$ is the singular chain complex of the space of homeomorphisms of $X$, fixed on $\bdy X$.
 \CH{X} \tensor \CH{X} \tensor \bc_*(X) \ar[r]^<<<<<{\id \tensor e_X} \ar[d]^{\compose \tensor \id} & \CH{X} \tensor \bc_*(X) \ar[d]^{e_X} \\
 \CH{X} \tensor \bc_*(X) \ar[r]^{e_X} & \bc_*(X)
 }
 \end{equation*}
 \end{thm}
-\nn{if we need to save space, I think this next paragraph could be cut}
-Since the blob complex is functorial in the manifold $X$, this is equivalent to having chain maps
-$$ev_{X \to Y} : \CH{X \to Y} \tensor \bc_*(X) \to \bc_*(Y)$$
-for any homeomorphic pair $X$ and $Y$,
-satisfying corresponding conditions.
 \begin{proof}(Sketch.)
 The most convenient way to prove this is to introduce yet another homotopy equivalent version of
 the blob complex, $\cB\cT_*(X)$.
 Blob diagrams have a natural topology, which is ignored by $\bc_*(X)$.
 The statement can be generalized to arbitrary fibre bundles, and indeed to arbitrary maps
 (see \cite[\S7.1]{1009.5025}).
 \nn{Theorem \ref{thm:product} is proved in \S \ref{ss:product-formula}, and Theorem \ref{thm:gluing} in \S \ref{sec:gluing}.}
-\section{Applications}
+\section{Higher Deligne conjecture}
 \label{sec:applications}
-Finally, we give two applications of the above machinery.
-\begin{thm}[Mapping spaces]
-\label{thm:map-recon}
-Let $\pi^\infty_{\le n}(T)$ denote the $A_\infty$ $n$-category based on maps
-$B^n \to T$.
-(The case $n=1$ is the usual $A_\infty$-category of paths in $T$.)
-Then
-$$\bc_*(X; \pi^\infty_{\le n}(T)) \simeq \CM{X}{T}.$$
-\end{thm}
-This says that we can recover (up to homotopy) the space of maps to $T$ via blob homology from local data.
-Note that there is no restriction on the connectivity of $T$ as there is for the corresponding result in topological chiral homology \cite[Theorem 3.8.6]{0911.0018}.
-\todo{sketch proof}
 \begin{thm}[Higher dimensional Deligne conjecture]
 \label{thm:deligne}
 The singular chains of the $n$-dimensional surgery cylinder operad act on blob cochains.
 Since the little $n{+}1$-balls operad is a suboperad of the $n$-SC operad,
 Kevin Costello,
 Mike Freedman,
 Justin Roberts,
 and
 Peter Teichner.
-\nn{not full list from big paper, but only most significant names}
 We also thank the Aspen Center for Physics for providing a pleasant and productive
 environment during the last stages of this project.
 \end{acknowledgments}
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