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nLab > Latest Changes: stable (infinity,1)-category

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 12th 2010
    • (edited Jan 21st 2016)
    I edited stable (infinity,1)-category a bit:

    * rephrased the intro part, trying to make it more forcefully to the point (not claiming to have found the optimum, though)

    * added a dedicated section <a href="http://ncatlab.org/nlab/show/stable+(infinity%2C1)-category#the_homotopy_category_of_a_stable_category_triangulated_categories_7">The homotopy cat of a stable (oo,1)-cat: traingulated categories</a> to highlight the important statement here, which was previously a bit hidden in the main text.
    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMay 14th 2011

    I have added a remark to stable derivator about why the homotopy category of such acquires one triangulation and not the “negative” triangulation, a potentially confusing point (at least, to me).

    This remark would probably fit better at stable (∞,1)-category, since the “negating one morphism” operation makes more sense there than in a derivator. But currently that page doesn’t actually describe the construction of the triangulation, which is necessary for the remark to make sense, whereas the page stable derivator does.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 14th 2013
    • (edited Oct 14th 2013)

    I have added a pointer to introductory notes by Yonatan Harpaz on stable ∞\infty-categories. These are notes a kindly prepared for our group seminar last week.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2014

    Briefly added pointer to formalization of the enrichment over spectra by Gepner-Haugseng, but then my battery died (this here from my phone)

    • CommentRowNumber5.
    • CommentAuthoradeelkh
    • CommentTimeDec 30th 2014

    I have added some missing op’s to the section Stabilization and localization of presheaf (∞,1)(\infty,1)-categories, and updated the statement of Proposition 2 (it’s even a sufficient condition for stable + presentable).

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 21st 2016

    for ease of reference, I have copied over the discussion of the Schwede-Shipley result also to stable infinity-category – Stabilization and localization

    • CommentRowNumber7.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 27th 2020

    Mentioned stable quasicategories.

    diff, v58, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 17th 2021
    • (edited Sep 17th 2021)

    the entry has been referring to a reference

    without giving a link. Probably this was

      http://www.math.uni-bonn.de/people/schwede/EnhancedSeminar.pdf

    which however is dead, and the WaybackMachine did not keep a copy. Does anyone have the file? Or its new location?

    diff, v62, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeSep 17th 2021
    • (edited Sep 17th 2021)

    Stefan Schwede has kindly provided a new copy of the missing file, which I have now uploaded to the nLab: ncatlab.org/nlab/show/files/Schwede_EnhancedSeminar.pdf

    (thanks to Bastiaan Cnossen, via AlgTop Discord, here)

    diff, v63, current

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