From: "Stephen Lack" <S.Lack@uws.edu.au>
To: <categories@mta.ca>
Subject: Re: Bicomma objects
Date: Wed, 25 Jul 2007 09:54:22 +1000 [thread overview]
Message-ID: <E1IDg2v-0004c8-DT@mailserv.mta.ca> (raw)
Dear Steve,
A bicomma object is a bicategorical limit, so determined only
up to equivalence. A comma object is a strict limit, so determined
up to isomorphism.
In the case of Cat, comma objects are just the usual comma categories
(strictly speaking, anything isomorphic to the comma category), while
anything equivalent to the comma category will be a bicomma object.
So any comma object is also a bicomma object, but the converse is false.
Moreover, there are 2-categories in which bicomma objects exist but
comma objects do not.
The situation with pullbacks, by the way, is slightly different. It is
not the case that every pullback is a bipullback (but there is a paper
of Joyal and Street giving a sufficient condition for a pullback to be
a bipullback).
Steve.
-----Original Message-----
From: cat-dist@mta.ca on behalf of Steve Vickers
Sent: Wed 25/07/2007 2:02 AM
To: categories@mta.ca
Subject: categories: Bicomma objects
What is the difference between a bicomma object and a comma object
(a.k.a. lax pullback)?
Steve.
next reply other threads:[~2007-07-24 23:54 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2007-07-24 23:54 Stephen Lack [this message]
-- strict thread matches above, loose matches on Subject: below --
2007-07-24 16:02 Steve Vickers
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=E1IDg2v-0004c8-DT@mailserv.mta.ca \
--to=s.lack@uws.edu.au \
--cc=categories@mta.ca \
/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).