Representing the deformation \(\infty\)-groupoid (Q2279053)

The goal of this paper is to introduce a version of the deformation \(\infty\)-groupoid associated to a homotopy Lie algebra which is weakly equivalent to the Deligne-Hinich \(\infty\)-groupoid, which is a Kan complex, which is contained in the Getzler \(\infty\)-groupoid \(\gamma_\bullet\) and which is represented by a universal cosimplicial object in the case of differential graded Lie algebras.