  It is well-known that a Lie algebroid A is equivalently described by a degree
1 Q-manifold M. We study distributions on M, giving a characterization in terms
of A. We show that involutive Q-invariant distributions on M correspond
bijectively to IM-foliations on A (the infinitesimal version of Mackenzie's
ideal systems). We perform reduction by such distributions, and investigate how
they arise from non-strict actions of strict Lie 2-algebras on M.
