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5 \section{$n$-categories (maybe)} |
5 \section{$n$-categories (maybe)} |
6 \label{sec:ncats} |
6 \label{sec:ncats} |
7 |
7 |
8 \nn{experimental section. maybe this should be rolled into other sections. |
8 \nn{experimental section. maybe this should be rolled into other sections. |
9 maybe it should be split off into a separate paper.} |
9 maybe it should be split off into a separate paper.} |
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10 |
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11 \nn{comment somewhere that what we really need is a convenient def of infty case, including tensor products etc. |
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12 but while we're at it might as well do plain case too.} |
10 |
13 |
11 \subsection{Definition of $n$-categories} |
14 \subsection{Definition of $n$-categories} |
12 |
15 |
13 Before proceeding, we need more appropriate definitions of $n$-categories, |
16 Before proceeding, we need more appropriate definitions of $n$-categories, |
14 $A_\infty$ $n$-categories, modules for these, and tensor products of these modules. |
17 $A_\infty$ $n$-categories, modules for these, and tensor products of these modules. |
901 \item say something about unoriented vs oriented vs spin vs pin for $n=1$ (and $n=2$?) |
904 \item say something about unoriented vs oriented vs spin vs pin for $n=1$ (and $n=2$?) |
902 \item spell out what difference (if any) Top vs PL vs Smooth makes |
905 \item spell out what difference (if any) Top vs PL vs Smooth makes |
903 \item define $n{+}1$-cat of $n$-cats (a.k.a.\ $n{+}1$-category of generalized bimodules |
906 \item define $n{+}1$-cat of $n$-cats (a.k.a.\ $n{+}1$-category of generalized bimodules |
904 a.k.a.\ $n{+}1$-category of sphere modules); discuss Morita equivalence |
907 a.k.a.\ $n{+}1$-category of sphere modules); discuss Morita equivalence |
905 \item morphisms of modules; show that it's adjoint to tensor product |
908 \item morphisms of modules; show that it's adjoint to tensor product |
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909 (need to define dual module for this) |
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910 \item functors |
906 \end{itemize} |
911 \end{itemize} |
907 |
912 |
908 \nn{Some salvaged paragraphs that we might want to work back in:} |
913 \nn{Some salvaged paragraphs that we might want to work back in:} |
909 \hrule |
914 \hrule |
910 |
915 |