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222 \begin{rem} |
222 \begin{rem} |
223 Perhaps the most interesting case is when $Y$ is just a point; then we have a way of building an $A_\infty$ $n$-category from a topological $n$-category. We think of this $A_\infty$ $n$-category as a free resolution. |
223 Perhaps the most interesting case is when $Y$ is just a point; then we have a way of building an $A_\infty$ $n$-category from a topological $n$-category. We think of this $A_\infty$ $n$-category as a free resolution. |
224 \end{rem} |
224 \end{rem} |
225 |
225 |
226 There is a version of the blob complex for $\cC$ an $A_\infty$ $n$-category |
226 There is a version of the blob complex for $\cC$ an $A_\infty$ $n$-category |
227 instead of a garden variety $n$-category; this is described in \S \ref{sec:ainfblob}. |
227 instead of a topological $n$-category; this is described in \S \ref{sec:ainfblob}. |
228 |
228 |
229 \begin{property}[Product formula] |
229 \begin{property}[Product formula] |
230 \label{property:product} |
230 \label{property:product} |
231 Let $W$ be a $k$-manifold and $Y$ be an $n-k$ manifold. Let $\cC$ be an $n$-category. |
231 Let $W$ be a $k$-manifold and $Y$ be an $n-k$ manifold. Let $\cC$ be an $n$-category. |
232 Let $A_*(Y,\cC)$ be the $A_\infty$ $k$-category associated to $Y$ via blob homology (see Property \ref{property:blobs-ainfty}). |
232 Let $A_*(Y,\cC)$ be the $A_\infty$ $k$-category associated to $Y$ via blob homology (see Property \ref{property:blobs-ainfty}). |