A version of the Goldman–Millson theorem for filtered L∞L∞-algebras

In this paper we consider L∞L∞-algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an L∞L∞ quasi-isomorphism U:L→L˜ induces a weak equivalence between the Deligne–Getzler–Hinich (DGH) ∞-groupoids corresponding to L   and L˜, respectively. This paper may be considered as a modest addition to foundational paper [10] by Ezra Getzler.