equal
deleted
inserted
replaced
1259 We must define maps |
1259 We must define maps |
1260 \[ |
1260 \[ |
1261 \cE\cB_n^k \times A \times \cdots \times A \to A , |
1261 \cE\cB_n^k \times A \times \cdots \times A \to A , |
1262 \] |
1262 \] |
1263 where $\cE\cB_n^k$ is the $k$-th space of the $\cE\cB_n$ operad. |
1263 where $\cE\cB_n^k$ is the $k$-th space of the $\cE\cB_n$ operad. |
1264 \nn{need to finish this} |
1264 Let $(b, a_1,\ldots,a_k)$ be a point of $\cE\cB_n^k \times A \times \cdots \times A \to A$. |
|
1265 The $i$-th embedding of $b$ together with $a_i$ determine an element of $\cC(B_i)$, |
|
1266 where $B_i$ denotes the $i$-th little ball. |
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1267 Using composition of $n$-morphsims in $\cC$, and padding the spaces between the little balls with the |
|
1268 (essentially unique) identity $n$-morphism of $\cC$, we can construct a well-defined element |
|
1269 of $\cC(B^n) = A$. |
1265 |
1270 |
1266 If we apply the homotopy colimit construction of the next subsection to this example, |
1271 If we apply the homotopy colimit construction of the next subsection to this example, |
1267 we get an instance of Lurie's topological chiral homology construction. |
1272 we get an instance of Lurie's topological chiral homology construction. |
1268 \end{example} |
1273 \end{example} |
1269 |
1274 |