John wrote:
I forget if "Frobenius monoidal" is a precise synonym of "bilax monoidal".
Steve replied:
No it's not. Frobenius monoidal is to Frobenius algebras as bilax monoidal is to bialgebras.
In particular a Frobenius monoidal functor 1-->C is a Frobenius algebra in C; a bilax monoidal functor 1-->C is a bialgebra in C.
Okay, I should have guessed. So the normalized chains functor from simplicial abelian groups to chain complexes is both Frobenius monoidal and bilax monoidal? We were talking a while back about structures like the group algebra of a finite group, which is both a Frobenius algebra and a bialgebra. I guess that means every finite group gives a functor from the terminal category to Vect that's both Frobenius monoidal and bilax monoidal? Is there some slick way to understand why? Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]