nForum - Search Results Feed (Tag: chain)2024-05-24T00:17:26+00:00https://nforum.ncatlab.org/
Lussumo Vanilla & Feed Publisher
total complex under Dold-Kanhttps://nforum.ncatlab.org/discussion/6155/2014-08-11T14:04:57+00:002014-08-11T22:18:51+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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