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For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...

10 votes
Accepted

Primitive elements of a tensor product of bialgebras

Well first when we restrict to the case when $A, B$ are filtered (see Bourbaki for example), in this case $\log_{*}$ always converges at $Id$ (as $Id=e+I_+$, $e$ being the unit for the convolution, it …
Duchamp Gérard H. E.'s user avatar
3 votes

Cocommutativity, comultiplication and coalgebra maps

In short, this property is true only in the context of counital coalgebras and NOT otherwise. … Remark : It is transparent in terms of identities that the property is true for coassociative coalgebras with counits. …
Duchamp Gérard H. E.'s user avatar