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nLab > Latest Changes: Dold-Kan correspondence

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    • CommentRowNumber1.
    • CommentAuthorJohn Baez
    • CommentTimeNov 29th 2009
    I did a wee bit of editing of "Dold-Kan correspondence", trying to incorporate Kathryn Hess' wisdom into this page. A lot of this stuff involves the monoidal aspects of the Dold-Kan correspondence, but I was too lazy to edit the separate page "monoidal Dold-Kan correspondence". I would ideally like that page to focus equal attention to chain complexes as it now does to cochain complexes!
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2009
    • (edited Nov 29th 2009)

    I had added what was not there yet from Hess's comment to monoidal Dold-kan correspondence.

    That page has two main subsections: one on the simplicial/chain one on the cosimplicial/cochain version.

    It does actually state more detailed and powerful things about the simplicial version. The reason that the cosimplicial version looks longer is because it gives a detailed discussion of what is standard in the simplicial case: why the cochain Moore functor is also lax monoidal ,something that is never much discussed in the literature.

    Also, one motivation for this page is still this asymmetry: there are detailed results on how the simplicial/chain Dold-Kan correspondence is fully oo-monoidal in both directions. The existing results on this for the cosimplicial/cochain version is much weaker. I am still trying to find the full statement here.

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