From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: wlawvere <wlawvere@buffalo.edu>
Cc: categories@mta.ca
Subject: Re: Grothendieck toposes
Date: Wed, 9 Nov 2016 11:48:29 +0100 [thread overview]
Message-ID: <20161109104828.GA12958@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <E1c4Goq-0004eP-Dd@mlist.mta.ca>
What Eduardo means by "Giraud topos" is a category validating all
conditions of the Giraud theorem with the exception of having a small
generating family. These guys can be elementary toposes or not.
There is Freyd's example where objects are set X with an ordinal
indexed family of bijections from X to X and morphisms are maps commuting with
all these ordinal many maps. This is a locally small cocomplete
elementary topos lacking a s mall generating family.
In 2011 on this list Johnstone gave the example of a category which
superficially is like Freyd's example but the class many endomaps are
not required to be bijections. This category is also bicomplete and
locally small but it hasn't got a subobject classifier.
Thomas
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2016-11-09 10:48 UTC|newest]
Thread overview: 29+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-11-08 13:32 wlawvere
2016-11-09 10:48 ` Thomas Streicher [this message]
[not found] <a98ed351-1df6-4f7d-1977-7d82d5a9900b@cs.bham.ac.uk>
2016-11-09 15:01 ` Thomas Streicher
[not found] <8641_1478651661_58226F0D_8641_41_1_E1c4Goq-0004eP-Dd@mlist.mta.ca>
2016-11-09 2:35 ` Marta Bunge
2016-11-09 15:53 ` Patrik Eklund
-- strict thread matches above, loose matches on Subject: below --
2016-11-06 15:41 wlawvere
[not found] <YQBPR01MB061141EA2F53A36490E14F0ADFA50@YQBPR01MB0611.CANPRD01.PROD.OUTLOOK.COM>
2016-11-05 15:04 ` Joyal, André
2016-11-03 14:03 Townsend, Christopher
[not found] <YQBPR01MB0611BC0F9930A55EC2DFE2C8DFAF0@YQBPR01MB0611.CANPRD01.PROD.OUTLOOK.COM>
2016-10-31 11:27 ` Steve Vickers
2016-11-01 10:10 ` Clemens.BERGER
2016-11-01 10:30 ` Thomas Streicher
[not found] ` <30618_1477941855_58179A5F_30618_291_1_E1c1IA3-0007Te-Te@mlist.mta.ca>
2016-10-31 22:40 ` Marta Bunge
[not found] ` <YQBPR01MB0611528D9E09F09BEB7C14B8DFAE0@YQBPR01MB0611.CANPRD01.PROD.OUTLOOK.COM>
2016-11-01 15:33 ` Marta Bunge
2016-11-02 0:20 ` Michael Barr
[not found] ` <004501d23520$bce007f0$36a017d0$@oliviacaramello.com>
2016-11-02 18:34 ` Marta Bunge
2016-10-30 20:17 Marta Bunge
2016-11-01 15:16 ` Joyal, André
[not found] ` <23129f7a064fe24cddfc1414403dfe85@cs.umu.se>
2016-11-02 11:18 ` Marta Bunge
2016-11-02 15:09 ` Townsend, Christopher
2016-11-03 4:45 ` Eduardo Julio Dubuc
2016-11-03 19:36 ` Joyal, André
[not found] ` <YQBPR01MB0611FD1B0099E7F4D36C84D9DFA00@YQBPR01MB0611.CANPRD01.PROD.OUTLOOK.COM>
2016-11-02 17:50 ` majordomo
2016-11-02 19:15 ` Marta Bunge
[not found] ` <YQBPR01MB0611A198AF9A5F51AD5562E8DFA00@YQBPR01MB0611.CANPRD01.PROD.OUTLOOK.COM>
[not found] ` <313cc907380f63841975a95b12cb1856@cs.umu.se>
2016-11-03 10:17 ` Steve Vickers
[not found] ` <581B0EB3.4030304@cs.bham.ac.uk>
2016-11-03 11:13 ` Patrik Eklund
2016-10-28 19:08 David Yetter
2016-10-30 3:06 ` Michael Shulman
2016-10-30 19:39 ` Joyal, André
2016-10-27 11:07 Steve Vickers
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