On the developability of Lie subalgebroids

For a Lie groupoid G with algebroid g, one says that a subalgebroid h⊂g is developable if it can be integrated to a closed Lie subgroupoid of the universal covering groupoid of G. Under some additional hypotheses, we construct an algebroid b, depending on G and h, and prove that the developability of h is equivalent to the integrability of b. This result extends the Almeida–Molino obstruction to developability of foliations.