Abstract
In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study of the structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalence between the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in a braided monoidal category and the category of Hopf algebras in the non-strict braided monoidal category of left-left Yetter-Drinfeld modules over H.
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