Discussion of Homotopy Type Theory and Univalent Foundations
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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.


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  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

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