Deligne groupoid revisited
  We show that for a differential graded Lie algebra $\mathfrak{g}$ whose components vanish in degrees below -1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of $\mathfrak{g}$-valued differential forms introduced by V.Hinich. 
Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan
math.AT math.DG