Our goal is to introduce a smaller, but equivalent version of the deformation –groupoid associated to a homotopy Lie algebra. In the case of differential graded Lie algebras, we represent it by a universal cosimplicial object.
"Representing the deformation $\infty$–groupoid." Algebr. Geom. Topol. 19 (3) 1453 - 1476, 2019. https://doi.org/10.2140/agt.2019.19.1453