We show that for a differential graded Lie algebra g whose components vanish in degrees below -1 the nerve of the Deligne 2-groupoid is homotopy equivalent to the simplicial set of g-valued differential forms introduced by V.~Hinich.
Keywords: groupoid, $L_\infty$-algebra, simplicial nerve
2010 MSC: 18G55, 55U10
Theory and Applications of Categories, Vol. 30, 2015, No. 29, pp 1001-1016.