Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids

We construct Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids as a generalization of the theory for Hopf algebras. More precisely, we show that the categories of Hopf bimodules and Yetter-Drinfeld modules over a Hopf algebroid are equivalent (pre-)braided monoidal categories. Moreover, we also study the duality between finitely generated projective Yetter-Drinfeld modules.