Abstract
We describe infinitesimally Dirac groupoids via geometric objects that we call Dirac bialgebroids. In the two well-understood special cases of Poisson and presymplectic groupoids, the Dirac bialgebroids are equivalent to the Lie bialgebroids and IM--forms, respectively. In the case of multiplicative involutive distributions on Lie groupoids, we find new properties of infinitesimal ideal systems.
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