On 8/05/10 4:03 AM, "John Baez" <john.c.baez@gmail.com> wrote:
André Joyal wrote:
I wonder who first introduced the notion of bilax monoidal functor and when?
I believe that Aguiar and Mahajan were the first to formally introduce this concept, though the Alexander-Whitney-Eilenberg-MacLane example has been around for a long time.
This is also my belief.
On the n-Category Cafe, Kathryn Hess recently wrote:
The A-W/E-Z equivalences for the normalized chains functor are a special case of the strong deformation retract of chain complexes that was constructed by Eilenberg and MacLane in their 1954 Annals paper "On the groups H(¼,n). II". For any commutative ring R, they defined chain equivalences between the tensor product of the normalized chains on two simplicial R-modules and the normalized chains on their levelwise tensor product.
Steve Lack and I observed recently that the normalized chains functor is actually even Frobenius monoidal. We then discovered that Aguiar and Mahajan already had a proof of this fact in their recent monograph. :-)
I forget if "Frobenius monoidal" is a precise synonym of "bilax monoidal".
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. Steve.
Best, jb
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]