Braidings for Non-Split Tambara-Yamagami Categories over the Reals

Non-split Real Tambara-Yamagami categories are a family of fusion categories over the real numbers that were recently introduced and classified by Plavnik, Sanford, and Sconce. We consider which of these categories admit braidings, and classify the resulting braided equivalence classes. We also prove some new results about the split real and split complex Tambara-Yamagami Categories. V2: Final Section removed, to appear in Transformation Groups.