1029 Define $\cl{\cC}(W)$ as a vector space via

  1029 Define $\cl{\cC}(W)$ as a vector space via

  1030 \[

  1030 \[

  1031 	\cl{\cC}(W) = \bigoplus_{(x_i)} \psi_{\cC;W}(x_0)[m] ,

  1031 	\cl{\cC}(W) = \bigoplus_{(x_i)} \psi_{\cC;W}(x_0)[m] ,

  1032 \]

  1032 \]

  1033 where the sum is over all $m$-sequences $(x_i)$ and all $m$, and each summand is degree shifted by $m$. 

  1033 where the sum is over all $m$-sequences $(x_i)$ and all $m$, and each summand is degree shifted by $m$. 

  1035 We endow $\cl{\cC}(W)$ with a differential which is the sum of the differential of the $\psi_{\cC;W}(x_0)$

  1035 We endow $\cl{\cC}(W)$ with a differential which is the sum of the differential of the $\psi_{\cC;W}(x_0)$

  1036 summands plus another term using the differential of the simplicial set of $m$-sequences.

  1036 summands plus another term using the differential of the simplicial set of $m$-sequences.

  1037 More specifically, if $(a, \bar{x})$ denotes an element in the $\bar{x}$

  1037 More specifically, if $(a, \bar{x})$ denotes an element in the $\bar{x}$

  1038 summand of $\cl{\cC}(W)$ (with $\bar{x} = (x_0,\dots,x_k)$), define

  1038 summand of $\cl{\cC}(W)$ (with $\bar{x} = (x_0,\dots,x_k)$), define

  1039 \[

  1039 \[