759 \bc_*(X\bigcup_Y \selfarrow) \simeq \bc_*(X) \Tensor^{A_\infty}_{\mathclap{\bc_*(Y)}} \selfarrow

   759 \bc_*(X\bigcup_Y \selfarrow) \simeq \bc_*(X) \Tensor^{A_\infty}_{\mathclap{\bc_*(Y)}} \selfarrow

   760 \end{equation*}

   760 \end{equation*}

   761 \end{itemize}

   761 \end{itemize}

   762 \end{thm}

   762 \end{thm}

   763 

   763 

   764 

   767 

   765 We next describe the blob complex for product manifolds, in terms of the $A_\infty$ blob complex of the $A_\infty$ $n$-categories constructed as above.

   768 We next describe the blob complex for product manifolds, in terms of the $A_\infty$ blob complex of the $A_\infty$ $n$-categories constructed as above.

   766 

   769 

   767 \begin{thm}[Product formula]

   770 \begin{thm}[Product formula]

   768 \label{thm:product}

   771 \label{thm:product}