I am looking for a text or set of notes that discusses the relationship between the representation theory of Lie groups and associated vector bundles, preferably using modern categorical language. For example, in the answer to this question, Mike Skirvin states:
"...fixing a G-bundle determines an exact tensor functor from the category of representations of G to the category of vector bundles. There's a converse to this which says that giving an exact tensor functor from representations of G to vector bundles is equivalent to a G-bundle."
I would especially like a text that proves this and other results. For instance, I would also like to know results for associated bundles when we have a reduction of the structure group, etc.
