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Starting with a self-dual Hopf algebra H in a braided monoidal category S weconstruct a Z/2Z-graded monoidal category C = C_0 + C_1. The degree zerocomponent is the category Rep_S(H) of representations of H and the degree onecomponent is the category S. The extra structure on H needed to define theassociativity isomorphisms is a choice of self-duality map and cointegral,subject to certain conditions. We also describe rigid, braided and ribbonstructures on C in Hopf algebraic terms. Our construction permits a uniformtreatment of Tambara-Yamagami categories and categories related to symplecticfermions in conformal field theory.

Z/2Z-extensions of Hopf algebra module categories by their base categories