Galois extensions of braided tensor categories and braided crossed G-categories

We show that the authorʹs notion of Galois extensions of braided tensor categories [Adv. Math. 150 (2000) 151], see also [A. Bruguières, Math. Ann. 316 (2000) 215], gives rise to braided crossed G-categories, recently introduced for the purposes of 3-manifold topology [V.G. Turaev, Homotopy field theory in dimension 3 and crossed group-categories, arXiv: math.GT/0005291]. The Galois extensions are studied in detail, in particular we determine for which g G non-trivial objects of grade g exist in .