Tambara-Yamagami (TY) 1-categories provide the mathematical framework to describe the algebra of extended operators of (1+1)-d theories that admit a duality defect. In this talk I will define what is the generalization of TY 1-categories for fusion 2-categories, and how to construct them from fusion 2-categories that are group-theoretical. I will also explain that group-theoretical fusion 2-categories are completely characterized by the property that the braided fusion 1-category of endomorphisms of the monoidal unit is Tannakian. Using this characterization, I will show when a fusion 2-category admits a fiber 2-functor.