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Tambara and Yamagami investigated a simple set of fusion rules with only onenon-invertible object, and proved under which circumstances those rules couldbe given a coherent associator. We consider a generalization of such fusionrules to the setting where simple objects are no longer required to be splitsimple. Over the real numbers, this means that objects are either real,complex, or quaternionic. In this context, we prove a similar categorificationresult to the one of Tambara and Yamagami.

Tambara-Yamagami Categories over the Reals: The Non-Split Case