# Deligne groupoid revisited

## Paul Bressler, Alexander Gorokhovsky, Ryszard Nest and Boris Tsygan

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.

Published 2015-07-16.

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