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};

  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