Smooth functors vs. differential forms

@article{Schreiber2008SmoothFV,
  title={Smooth functors vs. differential forms},
  author={Urs Schreiber and Konrad Waldorf},
  journal={Homology, Homotopy and Applications},
  year={2008},
  volume={13},
  pages={143-203}
}
We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in several fields, namely as connections on (non-abelian) gerbes, as derivatives of smooth functors and as critical points in BF theory. We demonstrate further that our dictionary… 

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