Smooth Functors vs. Differential Forms
Differential Geometry
2011-07-20 v4 Category Theory
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 curvatures 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.
Cite
@article{arxiv.0802.0663,
title = {Smooth Functors vs. Differential Forms},
author = {Urs Schreiber and Konrad Waldorf},
journal= {arXiv preprint arXiv:0802.0663},
year = {2011}
}
Comments
75 pages, 1 figure; v2 with only minor changes; v3 has a layout improvement; v4 is the published version, with small improvements and a better proof of Lemma 2.6