  A degree 1 non-negative graded super manifold equipped with a degree 1 vector
field Q satisfying [Q, Q]=1, namely a so-called NQ-1 manifold is, in plain
differential geometry language, a Lie algebroid. We introduce a notion of
fibration for such super manifols, that essentially involves a complete
Ehresmann connection. As it is the case for Lie algebras, such fibrations turn
out not to be just locally trivial products. We also define homotopy groups and
prove the expected long exact sequence associated to a fibration. In
particular, Crainic and Fernandes's obstruction to the integrability of Lie
algebroids is interpreted as the image of a transgression map in this long
exact sequence.
