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

Starting with a self-dual Hopf algebra H in a braided monoidal category S we construct a Z/2Z-graded monoidal category C=C0+C1. The degree zero component is the category RepS(H) of representations of H and the degree one component is the category S. The extra structure on H needed to define the associativity isomorphisms is a choice of self-duality map and cointegral, subject to certain conditions. We also describe rigid, braided and ribbon structures on C in Hopf algebraic terms.Our construction permits a uniform treatment of Tambara-Yamagami categories and categories related to symplectic fermions in conformal field theory.