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817 When $X$ is an $k$-ball, |
817 When $X$ is an $k$-ball, |
818 define $\cC(X; c) = \bc^\cE_*(X\times F; c)$ |
818 define $\cC(X; c) = \bc^\cE_*(X\times F; c)$ |
819 where $\bc^\cE_*$ denotes the blob complex based on $\cE$. |
819 where $\bc^\cE_*$ denotes the blob complex based on $\cE$. |
820 \end{example} |
820 \end{example} |
821 |
821 |
822 This example will be essential for Theorem \ref{thm:product} below, which allows us to compute the blob complex of a product. |
822 This example will be used in Theorem \ref{thm:product} below, which allows us to compute the blob complex of a product. |
823 Notice that with $F$ a point, the above example is a construction turning a topological |
823 Notice that with $F$ a point, the above example is a construction turning a topological |
824 $n$-category $\cC$ into an $A_\infty$ $n$-category which we'll denote by $\bc_*(\cC)$. |
824 $n$-category $\cC$ into an $A_\infty$ $n$-category which we'll denote by $\bc_*(\cC)$. |
825 We think of this as providing a ``free resolution" |
825 We think of this as providing a ``free resolution" |
826 of the topological $n$-category. |
826 of the topological $n$-category. |
827 \nn{say something about cofibrant replacements?} |
827 \nn{say something about cofibrant replacements?} |