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205 \end{itemize} |
205 \end{itemize} |
206 \end{property} |
206 \end{property} |
207 |
207 |
208 |
208 |
209 |
209 |
210 \begin{property}[Relation to mapping spaces] |
210 \begin{property}[Mapping spaces] |
211 Let $\pi^\infty_{\le n}(W)$ denote the $A_\infty$ $n$-category based on maps |
211 Let $\pi^\infty_{\le n}(W)$ denote the $A_\infty$ $n$-category based on maps |
212 $B^n \to W$. |
212 $B^n \to W$. |
213 (The case $n=1$ is the usual $A_\infty$ category of paths in $W$.) |
213 (The case $n=1$ is the usual $A_\infty$ category of paths in $W$.) |
214 Then |
214 Then |
215 $$\bc_*(M, \pi^\infty_{\le n}(W) \simeq \CM{M}{W}.$$ |
215 $$\bc_*(M, \pi^\infty_{\le n}(W) \simeq \CM{M}{W}.$$ |