Cocycle deformations for weak Hopf algebras

In this paper we introduce a theory of multiplication alteration by two-cocycles for weak Hopf algebras. We show that, just like it happens for Hopf algebras, if H a weak Hopf algebra and H & sigma; its weak Hopf algebra deformation by a 2-cocycle & sigma;, there is a braided monoidal category equivalence between the categories of left-right Yetter-Drinfel'd modules HYDH and H & sigma; YDH & sigma;. As a consequence we get in this context that the category Rep(D(H)) of left modules over the Drinfel'd double D(H) can be identified with the category Rep(D(H & sigma;)) of left modules over the Drinfel'd double D(H & sigma;).