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nLab > Latest Changes: simplicial localization

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeApr 5th 2013

    Someone deleted the contents of the entry simplicial localization on th 4 April, then another reinstated it on the 5th. Curious!

    • CommentRowNumber2.
    • CommentAuthorZhen Lin
    • CommentTimeApr 5th 2013

    I added in the definition of “standard” simplicial localisation.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 5th 2013
    • (edited Apr 5th 2013)

    @ZhenLin: thanks! Great.

    I have added some hyperlinks.

    (I thought we did have an entry “relative category”, but apparently we don’t. But I think somewhere on the nLab these are discussed a little. Can’t search right now, as I have to run.)

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeMay 1st 2021
    I think there should include some dicussions about the unversal property of the simplicial localisations, e.g. Remark 2.2.1 of Bertrand Toën and Gabriele Vezzosi's paper Homotopical Algebraic Geometry I: Topos Theory.
    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 1st 2021

    You are invited to try your hand on something. Hit “edit” at the bottom of the page to edit the source.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2021

    added pointer to:

    diff, v36, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2021

    added statement (here) on Quillen equivalences inducing DK equivalences

    diff, v38, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 31st 2023
    • (edited May 31st 2023)

    added DOIs to all the Dwyer & Kan-references

    diff, v44, current

  9. Changed the proposition directly under “### Simplicial localization of model categories”: the equivalence of (∞,1)-categories between the (bifibrant subcategory of) a simplicial model category and its simplicial localization at the weak equivalences only works if you let the former be a sSet-category, not a Set-category. This is also what Dwyer-Kan have in their paper, see property (iv) on their first page.

    Arthur Pander Maat

    diff, v46, current

1 to 10 of 10

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