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3 \section{The blob complex for $A_\infty$ $n$-categories} |
3 \section{The blob complex for $A_\infty$ $n$-categories} |
4 \label{sec:ainfblob} |
4 \label{sec:ainfblob} |
5 \label{sec:gluing} |
5 \label{sec:gluing} |
6 |
6 |
7 Given an $A_\infty$ $n$-category $\cC$ and an $n$-manifold $M$, we define the blob |
7 Given an $A_\infty$ $n$-category $\cC$ and an $n$-manifold $M$, we define the blob |
8 complex $\bc_*(M)$ to the be the colimit $\cC(M)$ of Section \ref{sec:ncats}. |
8 complex $\bc_*(M)$ to the be the homotopy colimit $\cC(M)$ of Section \ref{sec:ncats}. |
9 \nn{say something about this being anticlimatically tautological?} |
9 \nn{say something about this being anticlimatically tautological?} |
10 We will show below |
10 We will show below |
11 \nn{give ref} |
11 \nn{give ref} |
12 that this agrees (up to homotopy) with our original definition of the blob complex |
12 that this agrees (up to homotopy) with our original definition of the blob complex |
13 in the case of plain $n$-categories. |
13 in the case of plain $n$-categories. |