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787 When $X$ is an $k$-ball, |
787 When $X$ is an $k$-ball, |
788 define $\cC(X; c) = \bc^\cE_*(X\times F; c)$ |
788 define $\cC(X; c) = \bc^\cE_*(X\times F; c)$ |
789 where $\bc^\cE_*$ denotes the blob complex based on $\cE$. |
789 where $\bc^\cE_*$ denotes the blob complex based on $\cE$. |
790 \end{example} |
790 \end{example} |
791 |
791 |
792 This example will be essential for Theorem \ref{product_thm} below, which allows us to compute the blob complex of a product. |
792 This example will be essential for Theorem \ref{thm:product} below, which allows us to compute the blob complex of a product. |
793 Notice that with $F$ a point, the above example is a construction turning a topological |
793 Notice that with $F$ a point, the above example is a construction turning a topological |
794 $n$-category $\cC$ into an $A_\infty$ $n$-category which we'll denote by $\bc_*(\cC)$. |
794 $n$-category $\cC$ into an $A_\infty$ $n$-category which we'll denote by $\bc_*(\cC)$. |
795 We think of this as providing a `free resolution' |
795 We think of this as providing a `free resolution' |
796 \nn{`cofibrant replacement'?} |
796 \nn{`cofibrant replacement'?} |
797 of the topological $n$-category. |
797 of the topological $n$-category. |