409 \[

   409 \[

   410 	\bc_*(Y\times W; \cC) \simeq \cl{\bc_*(Y;\cC)}(W).

   410 	\bc_*(Y\times W; \cC) \simeq \cl{\bc_*(Y;\cC)}(W).

   411 \]

   411 \]

   412 \end{thm:product}

   412 \end{thm:product}

   413 The statement can be generalized to arbitrary fibre bundles, and indeed to arbitrary maps

   413 The statement can be generalized to arbitrary fibre bundles, and indeed to arbitrary maps

   415 

   415 

   416 Fix a topological $n$-category $\cC$, which we'll omit from the notation.

   416 Fix a topological $n$-category $\cC$, which we'll omit from the notation.

   417 Recall that for any $(n-1)$-manifold $Y$, the blob complex $\bc_*(Y)$ is naturally an $A_\infty$ category.

   417 Recall that for any $(n-1)$-manifold $Y$, the blob complex $\bc_*(Y)$ is naturally an $A_\infty$ category.

   418 (See Appendix \ref{sec:comparing-A-infty} for the translation between topological $A_\infty$ $1$-categories and the usual algebraic notion of an $A_\infty$ category.)

   418 (See Appendix \ref{sec:comparing-A-infty} for the translation between topological $A_\infty$ $1$-categories and the usual algebraic notion of an $A_\infty$ category.)

   419 

   419