JournalscmhVol. 73, No. 4pp. 637–676

Cogroups in algebras over an operad are free algebras

  • Benoit Fresse

    Université de Nice, France
Cogroups in algebras over an operad are free algebras cover
Download PDF

Abstract

Let P\cal P be an operad defined over a field of characteristic zero. Let R be a cogroup in the category of complete P{\cal P}-algebras. In this article, we show that R is necessarily the completion of a free P{\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.

Cite this article

Benoit Fresse, Cogroups in algebras over an operad are free algebras. Comment. Math. Helv. 73 (1998), no. 4, pp. 637–676

DOI 10.1007/S000140050072