A Bicategory Approach to Differential Cohomology

Abstract: A bicategory approach to differential cohomology is presented. Based on the axioms of Bunke-Schick, a symmetric monoidal groupoid is associated to differential refinements of cohomology theories. It is proven that such differential refinements are unique up to equivalence of the corresponding symmetric monoidal groupoids and the existing uniqueness results for rationally-even theories are interpreted in this framework. Moreover we show how the bicategory formalism may be used to give a simple construction of a differential refinement for any generalized cohomology theory, based on a refinement of the Chern character to a strict transformation of bicategories.