nForum - Discussion Feed (total complex under Dold-Kan)2024-03-28T22:38:20+00:00https://nforum.ncatlab.org/
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Urs comments on "total complex under Dold-Kan" (49043)https://nforum.ncatlab.org/discussion/6155/?Focus=49043#Comment_490432014-08-11T22:18:51+00:002024-03-28T22:38:20+00:00Urshttps://nforum.ncatlab.org/account/4/
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 ...
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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maming comments on "total complex under Dold-Kan" (49036)https://nforum.ncatlab.org/discussion/6155/?Focus=49036#Comment_490362014-08-11T14:04:57+00:002024-03-28T22:38:20+00:00maminghttps://nforum.ncatlab.org/account/1281/
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 ...
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.
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