Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
  1. Correction of non-mathematical typo


    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.