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1103 is given by the composition maps of $\cC$. |
1103 is given by the composition maps of $\cC$. |
1104 This completes the definition of the functor $\psi_{\cC;W}$. |
1104 This completes the definition of the functor $\psi_{\cC;W}$. |
1105 |
1105 |
1106 Note that we have constructed, at the last stage of the above procedure, |
1106 Note that we have constructed, at the last stage of the above procedure, |
1107 a map from $\psi_{\cC;W}(x)$ to $\cl\cC(\bd M_m) = \cl\cC(\bd W)$. |
1107 a map from $\psi_{\cC;W}(x)$ to $\cl\cC(\bd M_m) = \cl\cC(\bd W)$. |
1108 |
1108 \nn{need to show at somepoint that this does not depend on choice of ball decomp} |
1109 |
1109 |
1110 If $k=n$ in the above definition and we are enriching in some auxiliary category, |
1110 If $k=n$ in the above definition and we are enriching in some auxiliary category, |
1111 we need to say a bit more. |
1111 we need to say a bit more. |
1112 We can rewrite the colimit as |
1112 We can rewrite the colimit as |
1113 \[ % \begin{equation} \label{eq:psi-CC} |
1113 \[ % \begin{equation} \label{eq:psi-CC} |