From: Matt Oliveri <atm...@gmail.com>
To: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: cubical type theory with UIP
Date: Fri, 28 Jul 2017 18:47:26 -0700 (PDT) [thread overview]
Message-ID: <55685b9e-8177-42f0-9cfc-69901115181f@googlegroups.com> (raw)
In-Reply-To: <CAOvivQyFLkhoGhFLVSA9uSsitXJszOXouxDih2Ph0e-1HLNxsw@mail.gmail.com>
[-- Attachment #1.1: Type: text/plain, Size: 1303 bytes --]
I'm confused. So you want a cubical type theory with only hsets? In what
sense would there be cubes, other than just points? I thoght OTT had
propositional extensionality. Though maybe that's only for strict props.
On Sunday, July 23, 2017 at 6:54:39 PM UTC-4, Michael Shulman wrote:
>
> I am wondering about versions of cubical type theory with UIP. The
> motivation would be to have a type theory with canonicity for
> 1-categorical semantics that can prove both function extensionality
> and propositional univalence. (I am aware of Observational Type
> Theory, which I believe has UIP and proves function extensionality,
> but I don't think it proves propositional univalence -- although I
> would be happy to be wrong about that.)
>
> Presumably we obtain a cubical type theory that's compatible with
> axiomatic UIP if in CCHM cubical type theory we postulate only a
> single universe of propositions. But I wonder about some possible
> refinements, such as:
>
> 1. In this case do we still need *all* the Kan composition and gluing
> operations? If all types are hsets then it seems like it ought to be
> unnecessary to have these operations at all higher dimensions.
>
> 2. Can it be enhanced to make UIP provable, such as by adding a
> computing K eliminator?
>
> Mike
>
[-- Attachment #1.2: Type: text/html, Size: 1521 bytes --]
next prev parent reply other threads:[~2017-07-29 1:47 UTC|newest]
Thread overview: 20+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-07-23 22:54 Michael Shulman
2017-07-29 1:47 ` Matt Oliveri [this message]
2017-07-29 2:25 ` [HoTT] " Jon Sterling
2017-07-29 7:29 ` Matt Oliveri
2017-07-29 6:19 ` Michael Shulman
2017-07-29 7:23 ` Matt Oliveri
2017-07-29 8:07 ` Michael Shulman
2017-07-29 10:19 ` Matt Oliveri
2017-07-29 11:08 ` Matt Oliveri
2017-07-29 21:19 ` Michael Shulman
[not found] ` <8f052071-09e0-74db-13dc-7f76bc71e374@cs.bham.ac.uk>
2017-07-31 3:49 ` Matt Oliveri
2017-07-31 15:50 ` Michael Shulman
2017-07-31 17:36 ` Matt Oliveri
2017-08-01 9:14 ` Neelakantan Krishnaswami
2017-08-01 9:20 ` Michael Shulman
2017-08-01 9:34 ` James Cheney
2017-08-01 16:26 ` Michael Shulman
2017-08-01 21:27 ` Matt Oliveri
2017-07-31 4:19 ` Matt Oliveri
2017-08-02 9:40 ` [HoTT] " Andrea Vezzosi
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=55685b9e-8177-42f0-9cfc-69901115181f@googlegroups.com \
--to="atm..."@gmail.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).