Björn Gohla, Univ. Porto
Tri-connections and trifunctors
It is well known that connections on a principal G-bundle over a manifold M can be represented by group homomorphisms LM->G, where LM is the loop group of M. Similarly, 2-connections can be seen as 2-functors from a 2-groupoid of points, paths and bigons in M to a 2-group G. In passing to dimension 3, that is, considering tri-connections, 3-groupoids are too rigid, instead one needs to consider Gray-groupoids, their morphisms and transformations of higher dimension. We will describe a groupoid structure for certain functors between a pair of Gray-categories and certain transformations between them.