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409 \[ |
409 \[ |
410 \bc_*(Y\times W; \cC) \simeq \cl{\bc_*(Y;\cC)}(W). |
410 \bc_*(Y\times W; \cC) \simeq \cl{\bc_*(Y;\cC)}(W). |
411 \] |
411 \] |
412 \end{thm:product} |
412 \end{thm:product} |
413 The statement can be generalized to arbitrary fibre bundles, and indeed to arbitrary maps |
413 The statement can be generalized to arbitrary fibre bundles, and indeed to arbitrary maps |
414 (see \S \ref{moddecss}). |
414 (see \S \ref{ss:product-formula}). |
415 |
415 |
416 Fix a topological $n$-category $\cC$, which we'll omit from the notation. |
416 Fix a topological $n$-category $\cC$, which we'll omit from the notation. |
417 Recall that for any $(n-1)$-manifold $Y$, the blob complex $\bc_*(Y)$ is naturally an $A_\infty$ category. |
417 Recall that for any $(n-1)$-manifold $Y$, the blob complex $\bc_*(Y)$ is naturally an $A_\infty$ category. |
418 (See Appendix \ref{sec:comparing-A-infty} for the translation between topological $A_\infty$ $1$-categories and the usual algebraic notion of an $A_\infty$ category.) |
418 (See Appendix \ref{sec:comparing-A-infty} for the translation between topological $A_\infty$ $1$-categories and the usual algebraic notion of an $A_\infty$ category.) |
419 |
419 |