A derived-geometric definition of p-form connections on infinity-bundles is given via splittings of the Atiyah L-infinity-algebroid, recovering Cech-Deligne cocycles for higher U(1)-bundles.
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Symmetries and Higher-Form Connections in Derived Differential Geometry
A derived-geometric definition of p-form connections on infinity-bundles is given via splittings of the Atiyah L-infinity-algebroid, recovering Cech-Deligne cocycles for higher U(1)-bundles.