  We extend the AKSZ formulation of the Poisson sigma model to more general
target spaces, and we develop the general theory of graded geometry for
poly-symplectic and poly-Poisson structures. In particular we prove a
Schwarz-type theorem and transgression for graded poly-symplectic structures,
recovering the action functional and the poly-symplectic structure of the
reduced phase space of the poly-Poisson sigma model, from the AKSZ
construction.
