Differential cohomology theories as sheaves of spectra

@article{Bunke2013DifferentialCT,
  title={Differential cohomology theories as sheaves of spectra},
  author={Ulrich Bunke and Thomas Nickelsen Nikolaus and Michael V{\"o}lkl},
  journal={Journal of Homotopy and Related Structures},
  year={2013},
  volume={11},
  pages={1-66}
}
We show that every sheaf on the site of smooth manifolds with values in a stable $$(\infty ,1)$$(∞,1)-category (like spectra or chain complexes) gives rise to a “differential cohomology diagram” and a homotopy formula, which are common features of all classical examples of differential cohomology theories. These structures are naturally derived from a canonical decomposition of a sheaf into a homotopy invariant part and a piece which has a trivial evaluation on a point. In the classical… 
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