Abstract
We show that if a smooth multiplicative subbundle$S\subseteq TG$ on a groupoid $G⇉P$ is involutive and satisfies completeness conditions, then its leaf space$G/S$ inherits a groupoid structure over the space of leaves of $TP\cap S$ in $P$. As an application, a special class of Dirac groupoids is shown toproject by forward Dirac maps to Poisson groupoids.
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