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Given a Hopf algebra $H$ and a projection $H\to A$ to a Hopf subalgebra, weconstruct a Hopf algebra $r(H)$, called the partial dualization of $H$, with aprojection to the Hopf algebra dual to $A$. This construction provides powerfultechniques in the general setting of braided monoidal categories. Theconstruction comprises in particular the reflections of generalized quantumgroups, arxiv:1111.4673 . We prove a braided equivalence between theYetter-Drinfel'd modules over a Hopf algebra and its partial dualization.

Partially dualized Hopf algebras have equivalent Yetter-Drinfel'd modules