Geodesic
Smooth functors vs. differential forms
Homology, homotopy, and applications, Tome 13 (2011) no. 1, pp. 143-203.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2011.v13.n1.a7
Classification : 18F15, 53C05, 55R65
Keywords: connection, gerbe, 2-group, path 2-groupoid, parallel transport 
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Urs Schreiber; Konrad Waldorf. Smooth functors vs. differential forms. Homology, homotopy, and applications, Tome 13 (2011) no. 1, pp. 143-203. doi : 10.4310/HHA.2011.v13.n1.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2011.v13.n1.a7/

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