From: nicolas tabareau <tabareau...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Cc: homotopyt...@googlegroups.com, matthie...@inria.fr
Subject: Re: Is [Equiv Type_i Type_i] contractible?
Date: Thu, 27 Oct 2016 13:18:30 -0700 (PDT) [thread overview]
Message-ID: <8564e3b5-1226-404e-a6ed-716c5519cdb0@googlegroups.com> (raw)
In-Reply-To: <CALgtc7gp1VhjzF4h5GxpPCcsj0VUiGu4vuwQrrODDQU9u0jO+w@mail.gmail.com>
[-- Attachment #1.1: Type: text/plain, Size: 900 bytes --]
Thanks all for the answer.
I think our question was more "is it compatible with univalence or
implied by univalence + some parametricity assumption ?".
Of course, assuming other axioms in the theory that allow to distinguish
between types makes it false.
Best,
On Thursday, October 27, 2016 at 5:15:45 PM UTC+2, Matthieu Sozeau wrote:
>
> Dear all,
>
> we've been stuck with N. Tabareau and his student Théo Winterhalter on
> the above question. Is it the case that all equivalences between a universe
> and itself are equivalent to the identity? We can't seem to prove (or
> disprove) this from univalence alone, and even additional parametricity
> assumptions do not seem to help. Did we miss a counterexample? Did anyone
> investigate this or can produce a proof as an easy corollary? What is the
> situation in, e.g. the simplicial model?
>
> -- Matthieu
>
[-- Attachment #1.2: Type: text/html, Size: 1742 bytes --]
prev parent reply other threads:[~2016-10-27 20:18 UTC|newest]
Thread overview: 14+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-10-27 15:15 Matthieu Sozeau
2016-10-27 15:19 ` [HoTT] " Martin Escardo
2016-10-27 15:38 ` Martin Escardo
2016-10-27 17:09 ` Nicolai Kraus
2016-10-27 17:08 ` Vladimir Voevodsky
2016-10-27 17:12 ` Ulrik Buchholtz
2016-10-27 19:44 ` [HoTT] " Richard Williamson
2016-10-27 20:38 ` Ulrik Buchholtz
2016-10-30 20:56 ` Richard Williamson
2016-10-31 10:00 ` Eric Finster
2016-10-31 13:07 ` MLTT with proof-relevant judgmental equality? Neel Krishnaswami
2016-10-31 21:43 ` [HoTT] " Andrej Bauer
2016-10-31 22:01 ` Neel Krishnaswami
2016-10-27 20:18 ` nicolas tabareau [this message]
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=8564e3b5-1226-404e-a6ed-716c5519cdb0@googlegroups.com \
--to="tabareau..."@gmail.com \
--cc="HomotopyT..."@googlegroups.com \
--cc="matthie..."@inria.fr \
/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).