We develop a method for generating the complete set of basic data under the
torsorial actions of H[Ο]2β(G,A) and H3(G,U(1)) on
a G-crossed braided tensor category CGΓβ, where
A is the set of invertible simple objects in the braided tensor
category C. When C is a modular tensor category, the
H[Ο]2β(G,A) and H3(G,U(1)) torsorial action gives a
complete generation of possible G-crossed extensions, and hence provides a
classification. This torsorial classification can be (partially) collapsed by
relabeling equivalences that appear when computing the set of G-crossed
braided extensions of C. The torsor method presented here reduces
these redundancies by systematizing relabelings by A-valued
1-cochains. We also use our methods to compute the composition rule of these
torsor functors.Comment: 34 pages, several figures; v2: added Sec V, VI, and minor correction