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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2010
    • (edited May 12th 2010)

    Maybe somebody can quickly help me out. I think I knew the answer to the following question, but now I must have gotten myself mixed up:

    let F:Δ×ΔAbF : \Delta \times \Delta \to Ab be a bi-cosimplicial abelian group and

    diagF nΔ nF n, diag F \simeq \int^{n} \Delta^n \cdot F_{n,\bullet}

    the corresponding cosimplicial group. From the Eilenberg-Zilber theorem we have that its cochain complex is the total complex of the double complex obtained from FF

    CdiagFTotCF. C diag F \simeq Tot C F \,.

    But what I need is instead such a statement for the end expression

    nC((Δ n))C(F n,) \int_n C(\mathbb{Z}(\Delta^n)) \otimes C(F_{n,\bullet})

    How is that related to TotCF ,Tot C F_{\bullet,\bullet}? Isn’t that isomorphic?