diff -r ea489bbccfbf -r 60a068a5be10 blob1.tex --- a/blob1.tex Fri Jun 27 04:24:25 2008 +0000 +++ b/blob1.tex Mon Jun 30 13:02:57 2008 +0000 @@ -54,7 +54,7 @@ % \DeclareMathOperator{\pr}{pr} etc. \def\declaremathop#1{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}} -\applytolist{declaremathop}{pr}{im}{id}{gl}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{Tet}{cat}{Diff}{sign}{supp}; +\applytolist{declaremathop}{pr}{im}{id}{gl}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{Tet}{cat}{Diff}{sign}{supp}{maps}; @@ -1039,11 +1039,31 @@ \section{Extension to ...} \nn{Need to let the input $n$-category $C$ be a graded thing -(e.g.~DGA or $A_\infty$ $n$-category).} +(e.g. DG $n$-category or $A_\infty$ $n$-category). +DG $n$-category case is pretty easy, I think, so maybe it should be done earlier?? +Also, $A_\infty$ stuff (this section) should go before gluing section.} + +\bigskip -\nn{maybe this should be done earlier in the exposition? -if we can plausibly claim that the various proofs work almost -the same with the extended def, then maybe it's better to extend late (here)} +Outline: +\begin{itemize} +\item recall defs of $A_\infty$ category (1-category only), modules, (self-) tensor product. +use graphical/tree point of view, rather than following Keller exactly +\item define blob complex in $A_\infty$ case; fat mapping cones? tree decoration? +\item topological $A_\infty$ cat def (maybe this should go first); also modules gluing +\item motivating example: $C_*(\maps(X, M))$ +\item maybe incorporate dual point of view (for $n=1$), where points get +object labels and intervals get 1-morphism labels +\end{itemize} + + + + + + + + + \section{What else?...}