...
--- a/preamble.tex Tue Jul 21 16:21:20 2009 +0000
+++ b/preamble.tex Tue Jul 21 18:45:18 2009 +0000
@@ -80,7 +80,7 @@
% Marginal notes in draft mode -----------------------------------
\newcommand{\scott}[1]{\stepcounter{comment}{{\color{blue} $\star^{(\arabic{comment})}$}}\marginpar{\color{blue} $\star^{(\arabic{comment})}$ \usefont{T1}{scott}{m}{n} #1 --S}} % draft mode
-\newcommand{\kevin}[1]{\stepcounter{comment}{\color{green} $\star^{(\arabic{comment})}$}\marginpar{\color{green} $\star^{(\arabic{comment})}$ #1 --K}} % draft mode
+\newcommand{\kevin}[1]{\stepcounter{comment}{\color[rgb]{.2,.5,.6} $\star^{(\arabic{comment})}$}\marginpar{\color{green} $\star^{(\arabic{comment})}$ #1 --K}} % draft mode
\newcommand{\comment}[1]{\stepcounter{comment}$\star^{(\arabic{comment})}$\marginpar{\tiny $\star^{(\arabic{comment})}$ #1}} % draft mode
\newcounter{comment}
\newcommand{\noop}[1]{}
--- a/text/ncat.tex Tue Jul 21 16:21:20 2009 +0000
+++ b/text/ncat.tex Tue Jul 21 18:45:18 2009 +0000
@@ -253,7 +253,23 @@
Taking singular chains converts a space-type $A_\infty$ $n$-category into a chain complex
type $A_\infty$ $n$-category.
+\medskip
+The alert reader will have already noticed that our definition of (plain) $n$-category
+is extremely similar to our definition of topological fields.
+The only difference is that for the $n$-category definition we restrict our attention to balls
+(and their boundaries), while for fields we consider all manifolds.
+\nn{also: difference at the top dimension; fix this}
+Thus a system of fields determines an $n$-category simply by restricting our attention to
+balls.
+The $n$-category can be thought of as the local part of the fields.
+Conversely, given an $n$-category we can construct a system of fields via
+\nn{gluing, or a universal construction}
+
+\nn{Next, say something about $A_\infty$ $n$-categories and ``homological" systems
+of fields.
+The universal (colimit) construction becomes our generalized definition of blob homology.
+Need to explain how it relates to the old definition.}
\medskip
@@ -275,9 +291,10 @@
\item traditional $n$-cat defs (e.g. *-1-cat, pivotal 2-cat) imply our def of plain $n$-cat
\item conversely, our def implies other defs
\item traditional $A_\infty$ 1-cat def implies our def
-\item ... and vice-versa
+\item ... and vice-versa (already done in appendix)
\item say something about unoriented vs oriented vs spin vs pin for $n=1$ (and $n=2$?)
\item spell out what difference (if any) Top vs PL vs Smooth makes
+\item explain relation between old-fashioned blob homology and new-fangled blob homology
\end{itemize}