Holonomies for connections with values in L-infinity algebras

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Given a flat connection on a manifold with values in a filtered L-infinity-algebra, we construct a morphism of coalgebras that generalizes the holonomies of flat connections with values in Lie algebras. The construction is based on Gugenheim's A-infinity version of de Rham's theorem, which in turn is based on Chen's iterated integrals. Finally, we discuss examples related to the geometry of configuration spaces of points in Euclidean space, and to generalizations of the holonomy representations of braid groups.