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).

]]>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]