equal
deleted
inserted
replaced
52 \def\calc#1{\expandafter\def\csname c#1\endcsname{{\mathcal #1}}} |
52 \def\calc#1{\expandafter\def\csname c#1\endcsname{{\mathcal #1}}} |
53 \applytolist{calc}QWERTYUIOPLKJHGFDSAZXCVBNM; |
53 \applytolist{calc}QWERTYUIOPLKJHGFDSAZXCVBNM; |
54 |
54 |
55 % \DeclareMathOperator{\pr}{pr} etc. |
55 % \DeclareMathOperator{\pr}{pr} etc. |
56 \def\declaremathop#1{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}} |
56 \def\declaremathop#1{\expandafter\DeclareMathOperator\csname #1\endcsname{#1}} |
57 \applytolist{declaremathop}{pr}{im}{id}{gl}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{Tet}{cat}{Diff}{sign}{supp}; |
57 \applytolist{declaremathop}{pr}{im}{id}{gl}{tr}{rot}{Eq}{obj}{mor}{ob}{Rep}{Tet}{cat}{Diff}{sign}{supp}{maps}; |
58 |
58 |
59 |
59 |
60 |
60 |
61 %%%%%% end excerpt |
61 %%%%%% end excerpt |
62 |
62 |
1037 |
1037 |
1038 |
1038 |
1039 \section{Extension to ...} |
1039 \section{Extension to ...} |
1040 |
1040 |
1041 \nn{Need to let the input $n$-category $C$ be a graded thing |
1041 \nn{Need to let the input $n$-category $C$ be a graded thing |
1042 (e.g.~DGA or $A_\infty$ $n$-category).} |
1042 (e.g. DG $n$-category or $A_\infty$ $n$-category). |
1043 |
1043 DG $n$-category case is pretty easy, I think, so maybe it should be done earlier?? |
1044 \nn{maybe this should be done earlier in the exposition? |
1044 Also, $A_\infty$ stuff (this section) should go before gluing section.} |
1045 if we can plausibly claim that the various proofs work almost |
1045 |
1046 the same with the extended def, then maybe it's better to extend late (here)} |
1046 \bigskip |
|
1047 |
|
1048 Outline: |
|
1049 \begin{itemize} |
|
1050 \item recall defs of $A_\infty$ category (1-category only), modules, (self-) tensor product. |
|
1051 use graphical/tree point of view, rather than following Keller exactly |
|
1052 \item define blob complex in $A_\infty$ case; fat mapping cones? tree decoration? |
|
1053 \item topological $A_\infty$ cat def (maybe this should go first); also modules gluing |
|
1054 \item motivating example: $C_*(\maps(X, M))$ |
|
1055 \item maybe incorporate dual point of view (for $n=1$), where points get |
|
1056 object labels and intervals get 1-morphism labels |
|
1057 \end{itemize} |
|
1058 |
|
1059 |
|
1060 |
|
1061 |
|
1062 |
|
1063 |
|
1064 |
|
1065 |
|
1066 |
1047 |
1067 |
1048 |
1068 |
1049 \section{What else?...} |
1069 \section{What else?...} |
1050 |
1070 |
1051 \begin{itemize} |
1071 \begin{itemize} |