From: Marta Bunge <martabunge@hotmail.com>
To: Mike Shulman <mshulman@ucsd.edu>, <categories@mta.ca>
Subject: RE: stacks (was: size_question_encore)
Date: Wed, 13 Jul 2011 05:16:46 -0400 [thread overview]
Message-ID: <E1Qh3jA-0005zL-U9@mlist.mta.ca> (raw)
In-Reply-To: <16988_1310523866_4E1D01DA_16988_150_1_CAOvivQw6wf9CV0bwd0SbOJ=_5umAcXhTGwVJbMp0tV3oHXk+SQ@mail.gmail.com>
Dear Mike,
Yes, AC is elementary. Of course, so is ASC by the same token. Quantifying over all epis is not a problem. Thanks for questioning me on that point. I remembered incorrectly what the problem was. Bob Pare and I wanted to posit something like the existence of a "representative (or universal) cover" as an axiom (RC), such that GT => RC => ASC, and also (ET + AC) => RC. We hoped to show that RC had good properties, and more importantly, that Eff satisfied it but this did not work. What is still open is whether Eff satisfies ASC.
All the best,
Marta
> Date: Tue, 12 Jul 2011 19:24:25 -0700
> Subject: Re: categories: RE: stacks (was: size_question_encore)
> From: mshulman@ucsd.edu
> To: marta.bunge@mcgill.ca
> CC: categories@mta.ca
>
> I guess I misunderstood what you meant by "elementary". You wanted a
> single statement that can be expressed in the internal logic of the
> topos? Many other properties that people refer to as "elementary",
> such as the existence of finite limits or power objects, are defined
> by quantifying over all objects and morphisms of the category in
> question. Is AC "elementary"?
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-07-13 9:16 UTC|newest]
Thread overview: 14+ messages / expand[flat|nested] mbox.gz Atom feed top
[not found] <CAOvivQyUb8LfzWP-+ecki2WV2Fq8_qm-vCA0GNiu_nkC31nF-w@mail.gmail.com>
2011-07-12 12:30 ` Marta Bunge
2011-07-12 14:33 ` Michael Shulman
[not found] ` <SNT101-W529E9B5A38EF9C90E0B787DF440@phx.gbl>
2011-07-12 18:45 ` Michael Shulman
[not found] ` <SNT101-W50F2D8CAE24ED9DBB14F95DF440@phx.gbl>
2011-07-13 2:24 ` Michael Shulman
[not found] ` <16988_1310523866_4E1D01DA_16988_150_1_CAOvivQw6wf9CV0bwd0SbOJ=_5umAcXhTGwVJbMp0tV3oHXk+SQ@mail.gmail.com>
2011-07-13 9:16 ` Marta Bunge [this message]
[not found] ` <SNT101-W37B84477F7D0AC1746F41CDF470@phx.gbl>
2011-07-15 6:51 ` Michael Shulman
2011-07-15 10:27 Marta Bunge
-- strict thread matches above, loose matches on Subject: below --
2011-07-12 19:56 Marta Bunge
2011-07-12 15:04 André Joyal
2011-07-12 19:12 ` Eduardo Dubuc
[not found] ` <alpine.LRH.2.00.1107141113440.7062@siskin.dpmms.cam.ac.uk>
2011-07-15 19:01 ` Eduardo Dubuc
2011-07-12 14:56 Marta Bunge
2011-07-10 13:30 size_question_encore André Joyal
2011-07-11 5:36 ` stacks (was: size_question_encore) David Roberts
[not found] ` <1310362598.4e1a8be6a7800@webmail.adelaide.edu.au>
2011-07-11 12:32 ` Marta Bunge
2011-07-12 1:20 ` Michael Shulman
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