  We present a connection between the BFV-complex (abbreviation for
Batalin-Fradkin-Vilkovisky complex) and the so-called strong homotopy Lie
algebroid associated to a coisotropic submanifold of a Poisson manifold. We
prove that the latter structure can be derived from the BFV-complex by means of
homotopy transfer along contractions. Consequently the BFV-complex and the
strong homotopy Lie algebroid structure are $L_{\infty}$ quasi-isomorphic and
control the same formal deformation problem.
  However there is a gap between the non-formal information encoded in the
BFV-complex and in the strong homotopy Lie algebroid respectively. We prove
that there is a one-to-one correspondence between coisotropic submanifolds
given by graphs of sections and equivalence classes of normalized Maurer-Cartan
elemens of the BFV-complex. This does not hold if one uses the strong homotopy
Lie algebroid instead.
