Some remarks on braided group reconstruction and braided doubles

The cross coproduct braided group Aut(C) (sic) B is obtained by Tannaka-Kre in reconstruction from C-B --> C for a braided group B in braided category C. We apply this construction to obtain partial solutions to two problems i n braided group theory, namely the tensor problem and the braided double. W e obtain Aut(C) (sic) Aut(C)congruent to Aut(C) (sic) Aut(C) and higher bra ided group 'spin chains'. The example B(R) (sic) B(R) (sic) ... (sic) B(R) is described explicitly by R-matrix relations. We also obtain Aut(C) (sic) Aut(C)* as a dual quasitriangular 'codouble' braided group by reconstructio n from the dual category C degrees --> C. General braided double crossprodu cts BC are also considered.