From: John Baez <john.c.baez@gmail.com>
To: categories <categories@mta.ca>
Subject: Re: bilax monoidal functors
Date: Sat, 8 May 2010 16:19:22 -0700 [thread overview]
Message-ID: <E1OBEEE-0000fp-5G@mailserv.mta.ca> (raw)
In-Reply-To: <C80B6E26.B13C%s.lack@uws.edu.au>
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/ ]
next prev parent reply other threads:[~2010-05-08 23:19 UTC|newest]
Thread overview: 18+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-05-07 18:03 John Baez
2010-05-08 2:23 ` Andre Joyal
2010-05-08 23:11 ` Michael Batanin
2010-05-10 16:12 ` Toby Bartels
[not found] ` <4BE5EF9C.1060907@ics.mq.edu.au>
2010-05-08 23:34 ` John Baez
2010-05-08 9:38 ` Steve Lack
[not found] ` <C80B6E26.B13C%s.lack@uws.edu.au>
2010-05-08 23:19 ` John Baez [this message]
-- strict thread matches above, loose matches on Subject: below --
2010-05-15 16:23 bilax_monoidal_functors Jeff Egger
2010-05-11 8:28 bilax_monoidal_functors?= Michael Batanin
2010-05-15 16:54 ` bilax_monoidal_functors Jeff Egger
2010-05-11 1:04 bilax_monoidal_functors Fred E.J. Linton
2010-05-09 16:26 bilax_monoidal_functors?= Andre Joyal
2010-05-10 19:28 ` bilax_monoidal_functors Jeff Egger
2010-05-13 17:17 ` bilax_monoidal_functors Michael Shulman
2010-05-15 1:05 ` bilax_monoidal_functors Andre Joyal
2010-05-08 3:27 RE : bilax monoidal functors John Baez
2010-05-10 10:28 ` Urs Schreiber
2010-05-11 3:17 ` bilax_monoidal_functors Andre Joyal
2010-05-14 14:34 ` bilax_monoidal_functors Michael Shulman
2010-05-08 1:05 bilax monoidal functors David Yetter
2010-05-06 23:02 Q. about " Steve Lack
2010-05-07 14:59 ` bilax " Joyal, André
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