  We develop a general procedure for reduction along strong Dirac maps, which
are a broad generalization of Poisson momentum maps. We recover a large number
of familiar constructions in Poisson and quasi-Poisson geometry, and we
introduce new examples of Poisson, quasi-Poisson, and Dirac reduced structures.
In particular, we obtain quasi-Poisson analogues of several classes of spaces
that are studied in geometric representation theory.
