  Given a braided tensor *-category C with conjugate (dual) objects and
irreducible unit together with a full symmetric subcategory S we define a
crossed product C\rtimes S. This construction yields a tensor *-category with
conjugates and an irreducible unit. (A *-category is a category enriched over
Vect_C with positive *-operation.) A Galois correspondence is established
between intermediate categories sitting between C and C\rtimes S and closed
subgroups of the Galois group Gal(C\rtimes S/C)=Aut_C(C\rtimes S) of C, the
latter being isomorphic to the compact group associated to S by the duality
theorem of Doplicher and Roberts. Denoting by D\subset C the full subcategory
of degenerate objects, i.e. objects which have trivial monodromy with all
objects of C, the braiding of C extends to a braiding of C\rtimes S iff
S\subset D. Under this condition C\rtimes S has no degenerate objects iff S=D.
If the original category C is rational (i.e. has only finitely many equivalence
classes of irreducible objects) then the same holds for the new one. The
category C\rtimes D is called the modular closure of C since in the rational
case it is modular, i.e. gives rise to a unitary representation of the modular
group SL(2,Z). (In passing we prove that every braided tensor *-category with
conjugates automatically is a ribbon category, i.e. has a twist.) If all simple
objects of S have dimension one the structure of the category C\rtimes S can be
clarified quite explicitly in terms of group cohomology.

Category Theory;High Energy Physics - Theory