Demeter Krupka - "Differential invariants in gauge theory".

The subject of this talk is the theory of differential invariants of a Lie group, based on the theory of jets. 
We discuss basic categories of manifolds, principal bundles and associated bundles. 
We define the concept of a G-natural functor and show that the natural transformations of G-natural functors 
are in one-to-one correspondence with G-equivariant mappings of type fibres of these functors. 

Finally, we discuss the concept of the jet prolongation of Lie group G and a principal G-bundle, and introduce 
a differential invariant as an equivariant mapping of the prolonged group. 
This gives an abstract framework for the theory of (scalar) differential G-invariants that are used 
as Lagrangians in the variational functionals of the gauge theory.