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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