Open AccessCogroups in algebras over an operad are free algebras
Author(s) -
Benoît Fresse
Publication year - 1998
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.1007/s000140050072
Subject(s) - mathematics , zero (linguistics) , pure mathematics , field (mathematics) , algebra over a field , combinatorics , linguistics , philosophy
. Let be an operad defined over a field of characteristic zero. Let R be a cogroup in the category of complete -algebras. In this article, we show that R is necessarily the completion of a free -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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