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We give the definition of left/right Post-Lie algebras and left/rightPost-Hopf algebras and establish a link between those objects. We get aCartier-Quillen-Milnor-Moore theorem for Post-Hopf algebras. We give anotherdescription for free Post-Lie algebras and a description for Post-Lie algebrasobtained from an associative product.

The Cartier-Quillen-Milnor-Moore theorem in the Post-Hopf case