From: Andrej Bauer <andrej...@andrej.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Yet another characterization of univalence
Date: Tue, 28 Nov 2017 10:40:32 +0100 [thread overview]
Message-ID: <CAB0nkh3SJTCbPEMwmtrkHpvC0xu9-yaUicO6j4vWizTZB4gz1Q@mail.gmail.com> (raw)
In-Reply-To: <6570d6a7-2d41-475e-aa7f-b9dc318e74a6@googlegroups.com>
> If univalence holds, then Id : X -> (X -> U) is an embedding.
>
> But If the K axiom holds, then again Id : X -> (X -> U) is an embedding.
>
> And hence there is no hope to deduce univalence from the fact that Id_X is
> an embedding for every X:U.
>
> (And, as a side remark, I can't see how to prove that Id_X is an embedding
> without using K or univalence.)
So you've invented a new axiom?
Escardo's axiom: Id : X → (X → U) is an embedding.
(We could call it Martin's axiom to create lots of confusion.)
With kind regards,
Andrej
next prev parent reply other threads:[~2017-11-28 9:40 UTC|newest]
Thread overview: 16+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-11-17 23:53 Martín Hötzel Escardó
2017-11-20 3:54 ` [HoTT] " y
2017-11-24 12:21 ` Martín Hötzel Escardó
2017-11-24 19:11 ` Martín Hötzel Escardó
2017-11-28 9:40 ` Andrej Bauer [this message]
2017-11-29 21:12 ` Evan Cavallo
[not found] ` <204e382a-efcf-cb13-006f-47fdbadd99a5@cs.bham.ac.uk>
2017-11-29 22:15 ` Evan Cavallo
2017-11-29 22:16 ` Martín Hötzel Escardó
2017-12-01 14:49 ` Martin Escardo
2017-12-01 14:53 ` Martín Hötzel Escardó
2017-12-09 0:27 ` Martín Hötzel Escardó
2017-12-18 22:58 ` Martín Hötzel Escardó
2017-12-19 3:36 ` Gershom B
2017-12-20 20:46 ` Martín Hötzel Escardó
2017-11-24 23:12 ` Martín Hötzel Escardó
2017-11-24 23:28 ` Martín Hötzel Escardó
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=CAB0nkh3SJTCbPEMwmtrkHpvC0xu9-yaUicO6j4vWizTZB4gz1Q@mail.gmail.com \
--to="andrej..."@andrej.com \
--cc="HomotopyT..."@googlegroups.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).