From: Thomas Streicher <stre...@mathematik.tu-darmstadt.de>
To: Jon Sterling <j...@jonmsterling.com>
Cc: HomotopyT...@googlegroups.com
Subject: Re: [HoTT] Impredicative set + function extensionality + proof irrelevance consistent?
Date: Tue, 12 Dec 2017 20:29:21 +0100 [thread overview]
Message-ID: <20171212192921.GA11564@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <1513084622.1768586.1202387232.03F5CC27@webmail.messagingengine.com>
> I think that unique choice holds in every topos, at least when you state
> it in the topos logic. This is in Mac Lane & Moerdijk as exercise 11 in
> chapter VI, Topoi And Logic.
>
> I'm a little confused now, but maybe this has to do with some subtle
> difference between the ordinary topos-theoretic subobject classifier,
> and the HoTT-style one which you get from univalence (as you describe).
Of course, toposes all validate AUC. Since in an arbitrary topos logic
is interpreted via the topos's Omega AUC holds then as well.
Univalence is something which will not hold in most toposes and if it
does one has to interpret Id in a way that it is not a proposition.
Thomas
next prev parent reply other threads:[~2017-12-12 19:29 UTC|newest]
Thread overview: 54+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-12-11 4:22 Kristina Sojakova
2017-12-11 11:42 ` [HoTT] " Jon Sterling
2017-12-11 12:15 ` Kristina Sojakova
2017-12-11 12:43 ` Jon Sterling
2017-12-11 14:28 ` Thomas Streicher
2017-12-11 14:32 ` Kristina Sojakova
2017-12-11 14:23 ` Thorsten Altenkirch
2017-12-12 10:15 ` Andrea Vezzosi
2017-12-12 11:03 ` Thorsten Altenkirch
2017-12-12 12:02 ` Thomas Streicher
2017-12-12 12:21 ` Thorsten Altenkirch
2017-12-12 13:17 ` Jon Sterling
2017-12-12 19:29 ` Thomas Streicher [this message]
2017-12-12 19:52 ` Martin Escardo
2017-12-12 23:14 ` Michael Shulman
2017-12-14 12:32 ` Thorsten Altenkirch
2017-12-14 18:52 ` Michael Shulman
2017-12-16 15:21 ` Thorsten Altenkirch
2017-12-17 12:55 ` Michael Shulman
2017-12-17 17:08 ` Ben Sherman
2017-12-17 17:16 ` Thorsten Altenkirch
2017-12-17 22:43 ` Floris van Doorn
2017-12-15 17:00 ` Thomas Streicher
2017-12-17 8:47 ` Thorsten Altenkirch
2017-12-17 10:21 ` Thomas Streicher
2017-12-17 11:39 ` Thorsten Altenkirch
2017-12-18 7:41 ` Matt Oliveri
2017-12-18 10:00 ` Michael Shulman
2017-12-18 11:55 ` Matt Oliveri
2017-12-18 16:24 ` Michael Shulman
2017-12-18 20:08 ` Matt Oliveri
2017-12-18 10:10 ` Thorsten Altenkirch
2017-12-18 11:17 ` Matt Oliveri
2017-12-18 12:09 ` Matt Oliveri
2017-12-18 11:52 ` Thomas Streicher
2017-12-19 11:26 ` Thorsten Altenkirch
2017-12-19 13:52 ` Andrej Bauer
2017-12-19 14:44 ` Thorsten Altenkirch
2017-12-19 15:31 ` Thomas Streicher
2017-12-19 16:10 ` Thorsten Altenkirch
2017-12-19 16:31 ` Thomas Streicher
2017-12-19 16:37 ` Thorsten Altenkirch
2017-12-20 11:00 ` Thomas Streicher
2017-12-20 11:16 ` Thorsten Altenkirch
2017-12-20 11:41 ` Thomas Streicher
2017-12-21 0:42 ` Matt Oliveri
2017-12-22 11:18 ` Thorsten Altenkirch
2017-12-22 21:20 ` Martín Hötzel Escardó
2017-12-22 21:36 ` Martín Hötzel Escardó
2017-12-23 0:25 ` Matt Oliveri
2017-12-19 16:41 ` Steve Awodey
2017-12-20 0:14 ` Andrej Bauer
2017-12-20 3:55 ` Steve Awodey
[not found] ` <fa8c0c3c-4870-4c06-fd4d-70be992d3ac0@skyskimmer.net>
2017-12-14 13:28 ` Thorsten Altenkirch
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=20171212192921.GA11564@mathematik.tu-darmstadt.de \
--to="stre..."@mathematik.tu-darmstadt.de \
--cc="HomotopyT..."@googlegroups.com \
--cc="j..."@jonmsterling.com \
/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).