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nLab > Latest Changes: 2-group

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 22nd 2012
    • (edited Apr 22nd 2012)

    I looked at the entry 2-group today and found it strongly wanting. Now I have spent a few minutes with it, trying to bring it into better shape. While I think I did imporve it a little, there is clearly still lots of further room for improvement.

    Mainly what I did was add more on the intrinsic meaning and definition, more on the homotopical meaning, and more on the details of how crossed modules present the (2,1)(2,1)-category of 2-groups – amplifying the role of weak equivalences. And brief remarks on how all this generalizes to the case of 2-groups “with structure” hence internal to other ∞\infty-toposes than the terminal one.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 22nd 2012

    added an Examples-section on Equivalences of 2-groups.

    Almost done, but am being interrupted now..

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeApr 23rd 2012

    I fixed some typos. I could not see what was going wrong so replaced something by ∞Grp\infty Grp, which does come up with the right characters.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 23rd 2012

    Thanks, Tim!

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 31st 2016

    At 2-group where it says

    That should be

    w 2:BSO→B 2ℤ 2? w_2 : \mathbf{B}SO \to \mathbf{B}^2 \mathbb{Z}_2 ?
    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeMay 31st 2016
    • (edited May 31st 2016)

    Yep. And BSpin is the homotopy fibre of it.

    EDIT: now fixed.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 1st 2016

    Thanks for catching that. Weird.

    • CommentRowNumber8.
    • CommentAuthorJanPulmann
    • CommentTimeSep 25th 2019
    • (edited Sep 25th 2019)
    Hi,
    should the definition of the weak 2-group also demand that all morphisms are invertible? The definition in HDA V does that. Thanks!
    edit: to be clear, I mean the definition starting at https://ncatlab.org/nlab/show/2-group#weak_groups
    • CommentRowNumber9.
    • CommentAuthorUlrik
    • CommentTimeSep 26th 2019

    Fix the definitions of weak 2-groups

    diff, v40, current

    • CommentRowNumber10.
    • CommentAuthorUlrik
    • CommentTimeSep 26th 2019

    You’re right, so I just fixed these definitions, but maybe my phrasing is suboptimal. Feel free to edit, of course.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2021
    • (edited Jul 10th 2021)

    Added these pointers:

    Further on 2-group-extensions by the circle 2-group:

    of tori (see also at T-duality 2-group):

    of finite subgroups of SU(2) (to Platonic 2-groups):

    diff, v41, current

1 to 11 of 11

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