On de Rham Cohomology of Linear Categories
  We define the Chern map from the Grothendieck group of a linear category C to the de Rham cohomology of C with coefficients in a DG-category. In order to achieve our goal, we define the notion of connection on a C-module, and we show that the trace of the curvature of a connection is a de Rham cocycle, whose cohomology class does not depend on the choice of the connection. 
Andrei Chite\c{s}, M\u{a}d\u{a}lin Ciungu and Drago\c{s} \c{S}tefan
math.KT