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nLab: total complex under Dold-Kan

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    • CommentRowNumber1.
    • CommentAuthormaming
    • CommentTimeAug 11th 2014
    • (edited Aug 11th 2014)
    the nlab total+complex pages says:

    "The total chain complex is, under the Dold-Kan correspondence, equivalent to the diagonal of a bisimplicial set – see Eilenberg-Zilber theorem. As discussed at bisimplicial set, this is weakly homotopy equivalent to the total simplicial set of a bisimplicial set."

    Would it be that the total chain complex is **exactly** the total(i.e. codiagonal or $\bar{W}$) simplicial abelian group of the bisimplicial abelian group under Dold-Kan correspondence? Sorry if I am wrong.
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 11th 2014
    • (edited Aug 11th 2014)

    Thanks for the comment. Since I probably wrote this back when let me say that I don’t have the leisure right now to look into this, sorry. But if you think there is a useful stronger statement, why not write out the details here.

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