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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 1st 2017
   • (edited Jul 1st 2017)
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   Author: David_Corfield
   Format: MarkdownItexI see there's a new paper out [The General Linear 2-Groupoid](https://arxiv.org/abs/1706.07152) which works out the symmetries of a (2-term) graded vector space or bundle. I wonder how that compares with our old Klein 2-geometry efforts, such as Urs [here](https://golem.ph.utexas.edu/category/2006/10/klein_2geometry_vi.html#c005862). How have they ended up with a 2-groupoid where we managed with a 2-group? Maybe because we were just dealing with the skeletal 2-vector space case?

   I see there’s a new paper out The General Linear 2-Groupoid which works out the symmetries of a (2-term) graded vector space or bundle. I wonder how that compares with our old Klein 2-geometry efforts, such as Urs here.

   How have they ended up with a 2-groupoid where we managed with a 2-group? Maybe because we were just dealing with the skeletal 2-vector space case?

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeJul 1st 2017
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   Author: DavidRoberts
   Format: MarkdownItexThe objects of their 2-groupoid should be considered as (bundles of) 2-term chain complex structures on a fixed graded vector bundle. Fixing such a bundle of 2-term chain complexes, they get a 2-group.

   The objects of their 2-groupoid should be considered as (bundles of) 2-term chain complex structures on a fixed graded vector bundle. Fixing such a bundle of 2-term chain complexes, they get a 2-group.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 1st 2017
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   Author: David_Corfield
   Format: MarkdownItexAh OK, so an object involves a choice of differential $V_1 \to V_0$. Are there any benefits to collecting these together by underlying graded vector space? Why not just take as objects all 2-term chain complexes?

   Ah OK, so an object involves a choice of differential $V_1 \to V_0$. Are there any benefits to collecting these together by underlying graded vector space? Why not just take as objects all 2-term chain complexes?

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeJul 1st 2017
   • (edited Jul 1st 2017)
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   Author: Tim_Porter
   Format: MarkdownItexIt may be useful to look back at the thesis of Magnus Forrester-Barker [here](http://maths.bangor.ac.uk/research/ftp/theses/forrester-barker.pdf). He explored some of the same ideas from a nice simple perspective, but did not go so far. He has some elementary examples in a related (simpler) context.

   It may be useful to look back at the thesis of Magnus Forrester-Barker here. He explored some of the same ideas from a nice simple perspective, but did not go so far. He has some elementary examples in a related (simpler) context.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 1st 2017
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   Author: David_Corfield
   Format: MarkdownItexAh yes, the [Forrester-Barker 2-group](https://golem.ph.utexas.edu/category/2008/07/a_small_observation_1.html#c017663).

   Ah yes, the Forrester-Barker 2-group.

6. • CommentRowNumber6.
   • CommentAuthorTim_Porter
   • CommentTimeJul 1st 2017
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   Author: Tim_Porter
   Format: MarkdownItexDavid: thank you for that deep historical insight, ;-).

   David: thank you for that deep historical insight, ;-).

7. • CommentRowNumber7.
   • CommentAuthorAndrey Mikhovich
   • CommentTimeOct 27th 2017
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   Author: Andrey Mikhovich
   Format: TextDear Tim, did you hear anything concerning deformations of $\partial$ in a crossed module those do not change it up to N-dimensional representations?

   Dear Tim, did you hear anything concerning deformations of $\partial$ in a crossed module those do not change it up to N-dimensional representations?