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The Chern-Dold character of a cohomology theory E is a canonicaltransformation $E\rightarrow HV$ to ordinary cohomology. A spectrumrepresenting E gives homotopy theoretic cocycles for E, while HV can berepresented by singular cocycles. We construct a refinement of the Chern-Doldcharacter to a transformation of the cocycle categories that takes thehomotopical composition to the addition of singular cocycles. This is appliedto construct additive structures at the level of differential cocycles forgeneralized differential cohomology.

Refinements of the Chern-Dold Character: Cocycle Additions in Differential Cohomology