The work constructs adjusted connections on non-abelian bundle gerbes classified by Saemann's adjusted non-abelian differential cohomology and provides a new coordinate-free version of Tellez-Dominguez' lifting theorem to abelian 2-gerbes.
[Lur09] Jacob Lurie, Higher topos theory
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Adjusted connections on non-abelian bundle gerbes
The work constructs adjusted connections on non-abelian bundle gerbes classified by Saemann's adjusted non-abelian differential cohomology and provides a new coordinate-free version of Tellez-Dominguez' lifting theorem to abelian 2-gerbes.