We reformulate notions from the theory of quasi-Poisson g-manifolds in terms
of graded Poisson geometry and graded Poisson-Lie groups and prove that
quasi-Poisson g-manifolds integrate to quasi-Hamiltonian g-groupoids. We then
interpret this result within the theory of Dirac morphisms and multiplicative
Manin pairs, to connect our work with more traditional approaches, and also to
put it into a wider context suggesting possible generalizations.Comment: 39 page
