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An internal coproduct is described, which is compatible with Hoffman'squasi-shuffle product. Hoffman's quasi-shuffle Hopf algebra, withdeconcatenation coproduct, is a comodule-Hopf algebra over the bialgebra thusdefined. The relation with J. Ecalle's mould calculus, i.e. mould compositionand contracting arborification, is precised.

A comodule-bialgebra structure for word-series substitution and mould composition