Differentiation of Kan simplicial manifolds

Kan simplicial manifolds provide with a very explicit model for $L_\infty$-groupoids. Pavol Severa proposed a procedure of differentiation for these objects, yielding an $L_\infty$-algebroid, (an NQ-manifold). In the talk I will report on joint work with Du Li, Arne Wessel and Chenchang Zhu, where we have proven that this procedure always works. Recent work of Florian Dorsch shows that the Kan condition need not be explictly required for the procedure to work.