Abstract
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 provides a powerful tool to discuss the transgression of geometric objects to loop spaces.
Citation
Urs Schreiber. Konrad Waldorf. "Smooth functors vs. differential forms." Homology Homotopy Appl. 13 (1) 143 - 203, 2011.
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