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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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology 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 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

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 23rd 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded a References-section ([here](https://ncatlab.org/nlab/show/2-vector+bundle#AsAlgebraBundlesWithBimoduleBundlesBetweenThem)) with these pointers: *** The notion of 2-vector bundles based on regarding 2-vector spaces as algebras with bimodules between them ([here](https://ncatlab.org/nlab/show/2-vector+space#ReferencesAsAlgebrasWithBimodules)) is first discussed in * [[Urs Schreiber]], [[Konrad Waldorf]], §4.4 *Connections on non-abelian Gerbes and their Holonomy*, Theory Appl. Categ., **28** 17 (2013) 476-540 &lbrack;[arXiv:0808.1923](https://arxiv.org/abs/0808.1923), [tac:28-17](http://www.tac.mta.ca/tac/volumes/28/17/28-17abs.html)&rbrack; and much further developed in * [[Peter Kristel]], [[Matthias Ludewig]], [[Konrad Waldorf]], *The insidious bicategory of algebra bundles* &lbrack;[arXiv:2204.03900](https://arxiv.org/abs/2204.03900)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/2-vector+bundle/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/2-vector+bundle/3">v3</a>, <a href="https://ncatlab.org/nlab/show/2-vector+bundle">current</a>

   Added a References-section (here) with these pointers:

   ---

   The notion of 2-vector bundles based on regarding 2-vector spaces as algebras with bimodules between them (here) is first discussed in

   • Urs Schreiber, Konrad Waldorf, §4.4 Connections on non-abelian Gerbes and their Holonomy, Theory Appl. Categ., 28 17 (2013) 476-540 [arXiv:0808.1923, tac:28-17]

   and much further developed in

   • Peter Kristel, Matthias Ludewig, Konrad Waldorf, The insidious bicategory of algebra bundles [arXiv:2204.03900]

   diff, v3, current

2. • CommentRowNumber2.
   • CommentAuthorperezl.alonso
   • CommentTimeNov 22nd 2023
   • (edited Nov 22nd 2023)
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexI recall Konrad mentioning at the end of his talk back in March this year that some of the next steps included constructing a connection on a stringor bundle. Is there anything written out there about connections on 2-vector bundles in general, perhaps only for those represented by finite-dimensional algebra bundles? There's of course this discussion of connections on gerbes but wondering if there are any scattered comments on this somewhere (given that neither [here](https://arxiv.org/abs/2106.12198), nor [here](https://arxiv.org/abs/2204.03900), nor [here](https://arxiv.org/abs/2206.09797) do they address this point).

   I recall Konrad mentioning at the end of his talk back in March this year that some of the next steps included constructing a connection on a stringor bundle. Is there anything written out there about connections on 2-vector bundles in general, perhaps only for those represented by finite-dimensional algebra bundles? There’s of course this discussion of connections on gerbes but wondering if there are any scattered comments on this somewhere (given that neither here, nor here, nor here do they address this point).