Smooth functors vs. differential forms

By Urs Schreiber, K. Waldorf. 2008

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f62ee1ffb1aa8bb619f131b407c1412904f203ad