# 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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