Coverings in the Category of Principal Bundles.

We investigate the category of regular coverings of a given smooth principal bundle. A covering map of one principal bundle to another principal bundle is understood as a morphism in the category of principal bundles consisting of covering maps of their structural groups, total spaces and bases. The main results are: the construction of an invariant of a regular covering, which is a subsequence of the homotopy sequence of the base bundle; the existence theorem of a covering with a given invariant; criteria for morphisms and isomorphisms; a theorem on the automorphism group of a given covering. [ABSTRACT FROM AUTHOR]