equal
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inserted
replaced
410 \end{rem} |
410 \end{rem} |
411 |
411 |
412 \begin{proof} |
412 \begin{proof} |
413 The proof is again similar to that of Theorem \ref{thm:product}. |
413 The proof is again similar to that of Theorem \ref{thm:product}. |
414 |
414 |
415 We begin by constructing chain map $\psi: \cB^\cT(M) \to C_*(\Maps(M\to T))$. |
415 We begin by constructing a chain map $\psi: \cB^\cT(M) \to C_*(\Maps(M\to T))$. |
416 |
416 |
417 Recall that |
417 Recall that |
418 the 0-simplices of the homotopy colimit $\cB^\cT(M)$ |
418 the 0-simplices of the homotopy colimit $\cB^\cT(M)$ |
419 are a direct sum of chain complexes with the summands indexed by |
419 are a direct sum of chain complexes with the summands indexed by |
420 decompositions of $M$ which have their $n{-}1$-skeletons labeled by $n{-}1$-morphisms |
420 decompositions of $M$ which have their $n{-}1$-skeletons labeled by $n{-}1$-morphisms |