Discussion of Homotopy Type Theory and Univalent Foundations
 help / color / mirror / Atom feed
From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: Steve Awodey <awodey@cmu.edu>
Cc: "Michael Shulman" <shulman@sandiego.edu>,
	"\"Anders Mörtberg\"" <andersmortberg@gmail.com>,
	"Homotopy Type Theory" <homotopytypetheory@googlegroups.com>
Subject: Re: [HoTT] A unifying cartesian cubical type theory
Date: Sat, 16 Feb 2019 20:51:36 +0100	[thread overview]
Message-ID: <20190216195136.GA11255@mathematik.tu-darmstadt.de> (raw)
In-Reply-To: <4d63c003926b2c19e530c107c5b141cd.squirrel@webmail.mathematik.tu-darmstadt.de>

> > I think the idea is that the model structure is constructed / proved using
> > ideas from type theory (like univalence), rather than that it is a model
> > of type theory.  But I agree that the terminology is confusing.
> > The methodology is, I think, due to Christian Sattler ??? so maybe Sattler
> > model structure is more appropriate?
> 
> When the interval is fixed one might speak of minimal Cisinski model
> structure since it is the one with the fewest weak equivalences.
> Of course, Sattler studied them a lot so it's good name either.

Well, Coquand-Sattler might be better because it was first used in the
[CCHM] paper. From the many anodyne monos of the test model structure
one took just those which were syntactically convenient.
But, as far as I know the test model structure also gives rise to a
model of cubical TT because its more restrictive class off fibrations
suffices for interpreting sytax.

> Unfortunately, we don't know when minimal and test model structure concide.

Thomas

-- 
You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.

  reply	other threads:[~2019-02-16 19:51 UTC|newest]

Thread overview: 18+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2019-02-14 19:04 Anders Mortberg
2019-02-14 20:06 ` Andrew Pitts
2019-02-15 15:38   ` Anders Mörtberg
2019-02-15  8:16 ` Bas Spitters
2019-02-15 16:32   ` Anders Mörtberg
2019-02-16  0:01     ` Michael Shulman
2019-02-16  0:14       ` Steve Awodey
2019-02-16 12:30         ` streicher
2019-02-16 19:51           ` Thomas Streicher [this message]
2019-02-16 22:27             ` Steve Awodey
2019-02-17  9:43               ` Thomas Streicher
2019-02-17 14:14                 ` Licata, Dan
2019-02-16 21:58           ` Richard Williamson
2019-02-17  9:15             ` Thomas Streicher
2019-02-17 13:49               ` Richard Williamson
2019-02-18 14:05 ` [HoTT] " Andrew Swan
2019-02-18 15:31   ` Anders Mörtberg
2019-06-16 16:04     ` Anders Mörtberg

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=20190216195136.GA11255@mathematik.tu-darmstadt.de \
    --to=streicher@mathematik.tu-darmstadt.de \
    --cc=andersmortberg@gmail.com \
    --cc=awodey@cmu.edu \
    --cc=homotopytypetheory@googlegroups.com \
    --cc=shulman@sandiego.edu \
    /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).