From: Alan Jeffrey <ajeffrey@bell-labs.com>
To: Ross Street <ross.street@mq.edu.au>
Cc: <categories@mta.ca>
Subject: Re: Is "braided monoidal" a conservative extension of "lax braided monoidal"?
Date: Tue, 30 Nov 2010 17:43:22 -0600 [thread overview]
Message-ID: <E1PNmO7-0002Jt-0C@mlist.mta.ca> (raw)
In-Reply-To: <E1PNQxX-0002w5-Gy@mlist.mta.ca>
Indeed, a categorification of Garside's embedding of the positive braid
monoid into the braid group is exactly what I'm after. Unfortunately,
the nearest published result I've been able to find is:
Left-Garside categories, self-distributivity, and braids
Patrick Dehornoy
http://ambp.cedram.org/item?id=AMBP_2009__16_2_189_0
which shows this result for "the positive braid category", which has
natural numbers as objects, and braids as morphisms (and hence there are
only morphisms m --> n when m = n). The case of a freely generated lax
braided monoidal category isn't covered, although it may follow similarly.
There's a couple of related works:
Garside categories, periodic loops and cyclic sets
David Bessis
http://arxiv.org/abs/math/0610778
Garside and locally Garside categories
François Digne and Jean Michel
http://arxiv.org/abs/math/0612652
but they don't appear to have exactly the categorification of Garside
either.
A.
On 11/29/2010 04:24 PM, Ross Street wrote:
> Dear Alan
> The positive braid monoid is a Garside monoid and it embeds
> in the braid group.
> (It is not generally true that a monoid embeds in its group of
> fractions.
> There is a literature on Garside monoids.)
> I think this may be what you need.
> Ross
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
prev parent reply other threads:[~2010-11-30 23:43 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2010-11-29 16:34 Alan Jeffrey
[not found] ` <E1PNQxX-0002w5-Gy@mlist.mta.ca>
2010-11-30 23:43 ` Alan Jeffrey [this message]
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1PNmO7-0002Jt-0C@mlist.mta.ca \
--to=ajeffrey@bell-labs.com \
--cc=categories@mta.ca \
--cc=ross.street@mq.edu.au \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).