This is about an article of ours, in preparation
Domenico Fiorenza, Hisham Sati, Urs Schreiber,
Twisted differential structures
on twisted differential c-structures: twisted principal ∞-bundles with ∞-connections.
Central examples are
twisted differential spin structures;
twisted differential string structures;
twisted differential fivebrane structures.
differential T-duality pairs
differential cohomology in a cohesive topos
Quantum gauge field theory in Cohesive homotopy type theory
Principal ∞-bundles -- theory, presentations and applications
L-∞ algebra connections
Cech cocycles for differential characteristic classes
Twisted Differential String and Fivebrane Structures
The moduli 3-stack of the C-field
Higher Chern-Weil Derivation of AKSZ Sigma-Models
nonabelian 7d Chern-Simons theory and the 5-brane
Higher geometric prequantum theory
See differential cohomology in a cohesive topos -- references .