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The perturbation lemma and the homotopy transfer for L-infinity algebras is proved in a elementary way by using a relative version of the ordinary perturbation lemma for chain complexes and the coalgebra perturbation lemma.
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K. Fukaya: Deformation theory, homological algebra and mirror symmetry. Geometry and physics of branes (Como, 2001), Ser. High Energy Phys. Cosmol. Gravit., IOP Bristol (2003) 121-209. Electronic version available at http://www.math.kyoto-u.ac.jp/%7Efukaya/fukaya.html
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