Quantization of Quasi-Presymplectic Groupoids and their Hamiltonian Spaces

We study the prequantization of quasi-presymplectic groupoids and their Hamiltonian spaces using $S^1$-gerbes. We give a geometric description of the integrality condition. As an application, we study the prequantization of the quasi-Hamiltonian $G$-spaces of Alekseev–Malkin–Meinrenken.