1224 \label{ex:e-n-alg}

  1224 \label{ex:e-n-alg}

  1225 Let $A$ be an $\cE\cB_n$-algebra.

  1225 Let $A$ be an $\cE\cB_n$-algebra.

  1226 Note that this implies a $\Diff(B^n)$ action on $A$, 

  1226 Note that this implies a $\Diff(B^n)$ action on $A$, 

  1227 since $\cE\cB_n$ contains a copy of $\Diff(B^n)$.

  1227 since $\cE\cB_n$ contains a copy of $\Diff(B^n)$.

  1228 We will define a strict $A_\infty$ disk-like $n$-category $\cC^A$.

  1228 We will define a strict $A_\infty$ disk-like $n$-category $\cC^A$.

  1229 If $X$ is a ball of dimension $k<n$, define $\cC^A(X)$ to be a point.

  1230 If $X$ is a ball of dimension $k<n$, define $\cC^A(X)$ to be a point.

  1230 In other words, the $k$-morphisms are trivial for $k<n$.

  1231 In other words, the $k$-morphisms are trivial for $k<n$.

  1231 If $X$ is an $n$-ball, we define $\cC^A(X)$ via a colimit construction.

  1232 If $X$ is an $n$-ball, we define $\cC^A(X)$ via a colimit construction.

  1232 (Plain colimit, not homotopy colimit.)

  1233 (Plain colimit, not homotopy colimit.)

  1233 Let $J$ be the category whose objects are embeddings of a disjoint union of copies of 

  1234 Let $J$ be the category whose objects are embeddings of a disjoint union of copies of 

  1246 $\cC(X)$ are trivial (single point) for $k<n$, gives rise to 

  1247 $\cC(X)$ are trivial (single point) for $k<n$, gives rise to 

  1247 an $\cE\cB_n$-algebra.

  1248 an $\cE\cB_n$-algebra.

  1248 %\nn{The paper is already long; is it worth giving details here?}

  1249 %\nn{The paper is already long; is it worth giving details here?}

  1249 % According to the referee, yes it is...

  1250 % According to the referee, yes it is...

  1250 Let $A = \cC(B^n)$, where $B^n$ is the standard $n$-ball.

  1251 Let $A = \cC(B^n)$, where $B^n$ is the standard $n$-ball.

  1251 \nn{need to finish this}

  1257 \nn{need to finish this}

  1252 

  1258 

  1253 If we apply the homotopy colimit construction of the next subsection to this example, 

  1259 If we apply the homotopy colimit construction of the next subsection to this example, 

  1254 we get an instance of Lurie's topological chiral homology construction.

  1260 we get an instance of Lurie's topological chiral homology construction.

  1255 \end{example}

  1261 \end{example}