From: Michael Shulman <mshulman@ucsd.edu>
To: marta.bunge@mcgill.ca
Cc: categories@mta.ca
Subject: RE: stacks (was: size_question_encore)
Date: Tue, 12 Jul 2011 19:24:25 -0700 [thread overview]
Message-ID: <E1Qh3fd-0005rN-A0@mlist.mta.ca> (raw)
In-Reply-To: <SNT101-W50F2D8CAE24ED9DBB14F95DF440@phx.gbl>
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"?
On Tue, Jul 12, 2011 at 12:56 PM, Marta Bunge <martabunge@hotmail.com> wrote:
>
>
> Dear Mike,
>>
>> Does it not work to say that every internal category admits a weak
>> equivalence functor to an internal category which is a stack?
>
>
> Sure. This is so by Corollary 2.11 in Bunge-Pare. No problem with internal categories or internal weak equivalence functors of course. But how does one internalize the notion of a stack? It comes down to parametrizing all epimorphisms in the topos itself.
>
> All the best,Marta
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2011-07-13 2:24 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 [this message]
[not found] ` <16988_1310523866_4E1D01DA_16988_150_1_CAOvivQw6wf9CV0bwd0SbOJ=_5umAcXhTGwVJbMp0tV3oHXk+SQ@mail.gmail.com>
2011-07-13 9:16 ` Marta Bunge
[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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