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In this work we develop some aspects of the theory of Hopf algebras to thecontext of autonomous map pseudomonoids. We concentrate in the Hopf modules andthe Centre or Drinfel'd double. If $A$ is a map pseudomonoid in a monoidalbicategory \M, the analogue of the category of Hopf modules for $A$ is anEilenberg-Moore construction for a certain monad in$\mathbf{Hom}(\M^{\mathrm{op}},\mathbf{Cat})$. We study the existence of theinternalisation of this notion, called the Hopf module construction, byextending the completion under Eilenberg-Moore objects of a 2-category to aendo-homomorphism of tricategories on $\mathbf{Bicat}$.  Our main result is the equivalence between the existence of a leftdualization for $A$ ({\em i.e.}, $A$ is left autonomous) and the validity of ananalogue of the structure theorem of Hopf modules. In this case the Hopf moduleconstruction for $A$ always exists.  We use these results to study the lax centre of a left autonomous mappseudomonoid. We show that the lax centre is the Eilenberg-Moore constructionfor a certain monad on $A$ (one existing if the other does). If $A$ is alsoright autonomous, then the lax centre equals the centre. We look at theexamples of the bicategories of \V-modules and of comodules in \V, and obtainthe Drinfel'd double of a coquasi-Hopf algebra $H$ as the centre of $H$.

Hopf modules for autonomous pseudomonoids and the monoidal centre