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  1. Correction of non-mathematical typo

    Anonymous

    diff, v48, current

    • CommentRowNumber2.
    • CommentAuthorTim_Porter
    • CommentTimeOct 23rd 2021

    Removed the linking to Forrester-Barker as he is no longer active in mathematics and the grey link was not useful. The link to his PhD thesis remains.

    diff, v51, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 23rd 2022

    Added reference

    • Zhen Huan, 2-Representations of Lie 2-groups and 2-Vector Bundles (arXiv:2208.10042)

    Many years ago at the nnCafé I remember discussions on varieties of 2-vector space. The author here writes:

    There are other two types of 2-vector spaces, that people might be familiar with. One is the 2-vector space via categorification [BDR04] by Baez, Dundas and Rognes, and the other is Kapranov-Voevodsky’s 2-vector space [Kap99]. Philosophically [2ve13] our 2-vector spaces may be viewed as a sort of unification of these two.

    The reference [2ve13] is to 2-vector bundle.

    diff, v52, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2022
    • (edited Aug 23rd 2022)

    I have added more references to the actual References-section, such as to Kapranov & Voevodsky and to Baez & Crans, but also for instance to the review in BDSPV15.

    Then I took the liberty of making the following explicit (now here):


    The notion of 2-vector spaces with 2-linear maps between them as algebras with bimodules between them (subsuming the definition in Kapranov & Voevodsky 1991 as the special case of algebras that are direct sums of the ground field) is due to

    following earlier discussion in

    which is picked up in

    and further developed into a theory of 2-vector bundles (via algebra bundles with bundles of bimodules between them) in:

    Essentially the same notion also appears in:

    The notion is reviewed in a list of “standard” definitions in BDSPV15, without however referencing it.


    When BDSPV15 came out I expressed my surprise to Bruce B. who had been around when I promoted the notion and and knew that people certainly did not regard it as standard for a long time to come. I seem to remember that Bruce agreed to fix this in a revision, but it seems this article was never revised or published.

    diff, v53, current

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 24th 2022

    That was one of the original points of intersection at the nnCafé, your interest in 2-vector spaces and mine in Klein 2-geometry, as here.

    I see there’s me a little earlier chipping in here at The String Coffee Table to your post.