From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: categories@mta.ca
Subject: when is Fam (E) a topos?
Date: Wed, 19 Apr 2017 11:23:04 +0200 [thread overview]
Message-ID: <E1d0yx8-0006Ax-8X@mlist.mta.ca> (raw)
A couple of days ago I made the wrong claim that
> If BB is a topos and P : XX -> BB is a fibration then P is a fibration
> of toposes iff XX is a topos and P is a logical functor.
The following shows how wrong this claim is.
Let E be a topos then Fam(E) -> Set is certainly a fibered topos
but by Th.6.2.3 of Pieter Hofstra's Thesis Fam(E) is a topos iff E is
an atomic category (in the sense of Johnstone's 1977 book on Topos Theory,
exercise 12 on p. 257). But in atomic categories all morphisms are epic
and thus Fam(E) is a topos only if E is trivial.
Thus, for the motivating examples of fibred toposes the total category
is a topos only in the trivial case!
Thomas
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2017-04-19 9:23 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-04-19 9:23 Thomas Streicher [this message]
2017-04-21 9:01 ` Thomas Streicher
2017-04-22 16:35 ` Peter Johnstone
[not found] ` <alpine.DEB.2.10.1704221719340.10704@siskin.dpmms.cam.ac.uk>
2017-04-23 8:52 ` Thomas Streicher
2017-04-24 9:57 When is Fam(E) " Peter Johnstone
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=E1d0yx8-0006Ax-8X@mlist.mta.ca \
--to=streicher@mathematik.tu-darmstadt.de \
--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).