Discussion of Homotopy Type Theory and Univalent Foundations
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From: Andrew Pitts <Andrew.Pitts@cl.cam.ac.uk>
To: Homotopy Type Theory <homotopytypetheory@googlegroups.com>
Cc: Anders Mortberg <andersmortberg@gmail.com>,
	 "Prof. Andrew M Pitts" <andrew.pitts@cl.cam.ac.uk>
Subject: Re: [HoTT] A unifying cartesian cubical type theory
Date: Thu, 14 Feb 2019 20:06:15 +0000	[thread overview]
Message-ID: <CAK4K4j0qLQ_OLhc7XOUmdGT9CnLpS3ajbCxk8QSJS6xqB6uSeQ@mail.gmail.com> (raw)
In-Reply-To: <CAMWCppkw1yGyey0rDGnUawyiVN7TQ2cL6GKNfSXV__zuJvvONA@mail.gmail.com>

On Thu, 14 Feb 2019 at 19:05, Anders Mortberg <andersmortberg@gmail.com> wrote:
> The key idea is to weaken the notion of fibration from the cartesian
> Kan operations com^r->s so that they are not strictly the identity
> when r=s. Instead we introduce weak cartesian Kan operations that are
> only the identity function up to a path when r=s.

I was interested to read this, because I too use  that weakened form
of fibration in some work attempting to get a model of univalence
based only on composition of paths rather than more general Kan
filling operations — so far unpublished, because I can't quite see how
to get univalent universes to work (but seem frustratingly close to

Anyway, what I wanted to say is that perhaps one should call these
things "Dold fibrations" by analogy with the classic notion of Dold
fibration in topological spaces


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  reply	other threads:[~2019-02-14 20:06 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 [this message]
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
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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