From: F W Lawvere <wlawvere@buffalo.edu>
To: categories@mta.ca
Subject: Re: Undirected graph citation
Date: Thu, 2 Mar 2006 13:32:32 -0500 (EST) [thread overview]
Message-ID: <Pine.GSO.4.05.10603021317470.20737-100000@joxer.acsu.buffalo.edu> (raw)
As Clemens Berger reminds us, the category of small categories
is a reflective subcategory of simplicial sets, with a reflector that
preserves finite products. But as I mentioned, there is a similar
"advantage" for the Boolean algebra classifier (=presheaves on non-empty
finite cardinals, or "symmetric" simplicial sets):
The category of small groupoids is reflective in this topos, with the
reflector preserving finite products. Thus the Poincare' groupoid of a
simplicial complex is directly available. (The simplicial complexes are
merely the objects generated weakly by their points, a relation which
defines a cartesian closed reflective subcategory of any topos.)
It is not clear how one is to measure the loss or gain of combinatorial
information in composing the various singular and realization functors
between these different models. Is there such a measure?
Bill Lawvere
************************************************************
F. William Lawvere
Mathematics Department, State University of New York
244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA
Tel. 716-645-6284
HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere
************************************************************
next reply other threads:[~2006-03-02 18:32 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-03-02 18:32 F W Lawvere [this message]
2006-03-03 17:59 ` George Janelidze
2006-03-05 1:21 ` F W Lawvere
2006-03-05 19:15 ` George Janelidze
2006-03-06 20:08 ` wlawvere
2006-03-07 1:04 ` George Janelidze
2006-03-07 4:43 ` Vaughan Pratt
2006-03-03 9:04 Marco Grandis
2006-03-08 20:22 Dr. Cyrus F Nourani
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=Pine.GSO.4.05.10603021317470.20737-100000@joxer.acsu.buffalo.edu \
--to=wlawvere@buffalo.edu \
--cc=categories@mta.ca \
--cc=wlawvere@acsu.buffalo.edu \
/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).