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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 24th 2017

    I started a page on a recent preprint, categorified Dold-Kan correspondence.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 25th 2017
    • (edited Oct 25th 2017)

    Since this paper is taking initial steps to work out a categorified homological algebra and a categorified cohomology, is it time to categorify the cosmic cube?

    Are we entering a world where categorified cohomology concerns morphisms in an (,2)(\infty, 2)-topos? Maybe the stratified homotopy hypothesis becomes salient here, so that ’striation sheaves’ are geometric models for (,1)(\infty, 1)-categories with a fundamental exit path (,1)(\infty, 1)-category.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 25th 2017
    • (edited Oct 25th 2017)

    Would be good to add to categorified Dold-Kan correspondence a comment on how it is motivated by and subsumes and maybe sheds new light on various versions of the Waldhausen S-contruction, as Tobias Dyckerhoff explains in his introduction.

    (Myself no time.)

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 25th 2017

    Something along those lines now there.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 25th 2017

    Thanks!!

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 25th 2017

    I have also added a pointer under “related entries” at categorification. (That entry, of all entries here, is lacking some love. What about the ancient query box there? I think we can remove this and instead leave a coherent message.)