Re: bilax monoidal functors

[Andre Joyal <joyal.andre@uqam.ca>]

Dear John,


I am using the following terminology for
higher braided monoidal (higher) categories:

Monoidal< braided < 2-braided <.......<symmetric

A (n+1)-braided n-category is symmetric
according to your stabilisation hypothesis.

Is this a good terminology?

Best,
André


-------- Message d'origine--------
De: categories@mta.ca de la part de John Baez
Date: ven. 07/05/2010 14:03
À: categories
Objet : categories: bilax monoidal functors
 
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.

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(?,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".

Best,
jb


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