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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 21st 2017
    • (edited Feb 21st 2017)

    for the purposes of having direct links to it, I gave a side-remark at stable Dold-Kan correspondence its own page: rational stable homotopy theory, recording the equivalence

    (H)ModSpectraCh()

    I also added the claim that under this identification and that of classical rational homotopy theory then the derived version of the free-forgetful adjunction

    (dgcAlg2)/[0]SymcnUker(ε())Ch()

    models the stabilization adjunction (ΣΩ). But I haven’t type the proof into the entry yet.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 22nd 2017

    I have added to the beginning of the entry (rational stable homotopy theory) a remark that rational spectra are H-module spectra. Deserves to be further expanded.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 23rd 2017
    • (edited Feb 23rd 2017)

    In #1 I wrote:

    I also added the claim that [...] But I haven’t type the proof into the entry yet.

    Done now, here:

    The following composite total derived functors

    Ho(Spectra,fin)Ho(Ch,,fin)𝕃i2cn2Ho(Ch,>1,fin)()*Ho(Ch>1,fin)op((Uker(ε())))op(𝕃Sym/[0])opHo(dgcAlg>0,fin)/[0])opHo(Top,>1,fin)

    agree with the restriction of the stabilization infinity-adjunction

    SpectraΣΩGrpd*/

    to simply connected rational homotopy types of finite type.