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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 $(\infty, 2)$-topos? Maybe the stratified homotopy hypothesis becomes salient here, so that ’striation sheaves’ are geometric models for $(\infty, 1)$-categories with a fundamental exit path $(\infty, 1)$-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.)