#
Deligne groupoid revisited

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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.

http://www.tac.mta.ca/tac/volumes/30/29/30-29.pdf

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