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We introduce the notion of relational symplectic groupoid as a way tointegrate Poisson manifolds in general, following the construction through thePoisson sigma model (PSM) given by Cattaneo and Felder. We extend suchconstruction to the infinite dimensional setting, where we are able to describethe relational symplectic groupoid in terms of immersed Lagrangian Bannachsubmanifolds. This corresponds to a groupoid object in the "extended symplecticcategory" and it can be related to the ususal version of symplectic groupoidsvia reduction. We prove the existence of such an object for any Poissonmanifold and the uniqueness of a compatible Poisson structure on the base, fora special type of relational symplectic groupoids. We develop the notion ofequivalence, that allows us to compare finite and infinite dimensionalexamples.  We discuss some other extensions to different categories, where therelational construction still make sense, in an effort to understand bettergeometric quantization of symplectic manifolds in this new perspective.

Relational symplectic groupoids and Poisson sigma models with boundary