396 for example product boundary conditions or take the union over all boundary conditions.

   396 for example product boundary conditions or take the union over all boundary conditions.

   397 \nn{maybe should not emphasize this case, since it's ``better" in some sense

   397 \nn{maybe should not emphasize this case, since it's ``better" in some sense

   398 to think of these guys as affording a representation

   398 to think of these guys as affording a representation

   399 of the $n{+}1$-category associated to $\bd F$.}

   399 of the $n{+}1$-category associated to $\bd F$.}

   400 

   400 

   401 \end{itemize}

   403 \end{itemize}

   402 

   404 

   403 

   405 

   404 Examples of $A_\infty$ $n$-categories:

   406 Examples of $A_\infty$ $n$-categories:

   405 \begin{itemize}

   407 \begin{itemize}

   411 

   413 

   412 \item

   414 \item

   413 Given a plain $n$-category $C$, 

   415 Given a plain $n$-category $C$, 

   414 define $\cC(X; c) = \bc^C_*(X\times F; c)$, where $X$ is an $n$-ball

   416 define $\cC(X; c) = \bc^C_*(X\times F; c)$, where $X$ is an $n$-ball

   415 and $\bc^C_*$ denotes the blob complex based on $C$.

   417 and $\bc^C_*$ denotes the blob complex based on $C$.

   416 

   420 

   417 \end{itemize}

   421 \end{itemize}

   418 

   422 

   419 

   423 

   420 

   424