differential cohomology in an (∞,1)-topos -- survey
structures in an (∞,1)-topos
shape
cohomology
cocycle/characteristic class
twisted cohomology
principal ∞-bundle
∞-vector bundle
homotopy
covering ∞-bundles
Postnikov system
path ∞-groupoid
geometric realization
Galois theory
internal homotopy ∞-groupoid
Whitehead system
rational homotopy
∞-Lie algebroid
ordinary rational homotopy
internal rational homotopy
Chern-character
differential cohomology
flat differential cohomology
de Rham cohomology
de Rham theorem
relative theory over a base
relative homotopy theory
Lie theory
(…)
Background fields in twisted differential nonabelian cohomology
Differential twisted String and Fivebrane structures
D'Auria-Fre formulation of supergravity
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see differential cohomology in an (∞,1)-topos