Abstract.
Let \(\cal P\) be an operad defined over a field of characteristic zero. Let R be a cogroup in the category of complete \({\cal P}\)-algebras. In this article, we show that R is necessarily the completion of a free \({\cal P}\)-algebra. We also handle the case of cogroups in connected graded algebras over an operad, and the case of groups in connected graded coalgebras over an operad.
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Received: August 26, 1996 and final version, February 4, 1998
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Fresse, B. Cogroups in algebras over an operad are free algebras. Comment. Math. Helv. 73, 637–676 (1998). https://doi.org/10.1007/s000140050072
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DOI: https://doi.org/10.1007/s000140050072