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255 \end{equation*} |
255 \end{equation*} |
256 \end{itemize} |
256 \end{itemize} |
257 \end{property} |
257 \end{property} |
258 |
258 |
259 Finally, we state two more properties, which we will not prove in this paper. |
259 Finally, we state two more properties, which we will not prove in this paper. |
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260 \nn{revise this; expect that we will prove these in the paper} |
260 |
261 |
261 \begin{property}[Mapping spaces] |
262 \begin{property}[Mapping spaces] |
262 Let $\pi^\infty_{\le n}(T)$ denote the $A_\infty$ $n$-category based on maps |
263 Let $\pi^\infty_{\le n}(T)$ denote the $A_\infty$ $n$-category based on maps |
263 $B^n \to T$. |
264 $B^n \to T$. |
264 (The case $n=1$ is the usual $A_\infty$-category of paths in $T$.) |
265 (The case $n=1$ is the usual $A_\infty$-category of paths in $T$.) |