abstract: The deformation functor associated to a sheaf of Lie algebras L is naturally isomorphic to the deformation functor associated to the differential graded Lie algebra of global sections of a resolution of L by an acyclic sheaf of DGLAs. We describe a proof of this result based on a canonical L-infinity structure on the total complex of a semicosimplicial DGLA. Joint work with Elena Martinengo and Marco Manetti.