Cogroups in algebras over an operad are free algebras

Fresse, Benoit

doi:10.1007/s000140050072

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Commentarii Mathematici Helvetici

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Volume 73, Issue 4, 1998, pp. 637–676

DOI: 10.1007/s000140050072

Published online: 1998-12-31

Cogroups in algebras over an operad are free algebras

Benoit Fresse^[1]

(1) Université de Nice, France

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.

Keywords: Cogroup, operad

Fresse Benoit: Cogroups in algebras over an operad are free algebras. Comment. Math. Helv. 73 (1998), 637-676. doi: 10.1007/s000140050072