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We construct a natural morphism from the nerve MC_ (L) = MC (_ L) of a pronilpotent curved L_-algebra L to the simplicial subset _ (L) = MC (_ L, s_) of Maurer--Cartan element satisfying the Dupont gauge condition. This morphism equals the identity on the image of the inclusion _ (L) MC_ (L). The proof uses the extension of Berglund's homotopical perturbation theory for L_-algebras to curved L_-algebras. The morphism equals the holonomy for nilpotent Lie algebras. In a sequel to this paper, we use a cubical analogue ^ of to identify with higher holonomy for semiabelian curved -algebras.
Ezra Getzler (Tue,) studied this question.