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Atrium > Mathematics, Physics & Philosophy: Dold-Kan Correspondence for DGC's

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    • CommentRowNumber1.
    • CommentAuthorMirco Richter
    • CommentTimeMar 29th 2012

    Is there a Dold-Kan correspondence between differential graded coalgebras and something?

    in the nLab entry on L ∞L_\infty-algebras there is the bijection between degreewise finite dimensional differential graded algebras (in positive degrees) and their corresponding differential graded coalgebras. For DGA’s there is such a correspondence. …

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2012

    That correspondence between L ∞L_\infty-algebras and dg-algebras is an instance of Koszul duality of linear operads.

    • CommentRowNumber3.
    • CommentAuthorMirco Richter
    • CommentTimeMar 29th 2012
    • (edited Mar 29th 2012)

    So? What is the relation to my question? (I didn’t ask if there is a DK corresp. between L ∞L_\infty-algebras and DGA’s, obviously!)

    • CommentRowNumber4.
    • CommentAuthorMirco Richter
    • CommentTimeMar 29th 2012

    More like: Simplicial objects in the category of coalgebras are in correspondence with differential graded coalgebras seen by …

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 29th 2012
    • (edited Mar 29th 2012)

    There is some discussion of a co-monoidal Dold-Kan correspondence in this PhD thesis

    • The Dold-Kan Correspondence and Coalgebra Structures (pdf)
    • CommentRowNumber6.
    • CommentAuthorMirco Richter
    • CommentTimeMar 29th 2012

    thanks Urs…

1 to 6 of 6

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