From: "Rafaël Bocquet" <rafael.bocquet@ens.fr>
To: Kristina Sojakova <sojakova.kristina@gmail.com>,
Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] HoTT with extensional equality
Date: Tue, 7 Jan 2020 23:03:14 +0100 [thread overview]
Message-ID: <7d1235e5-76ac-2a7d-9317-21d30f6973ad@ens.fr> (raw)
In-Reply-To: <8de08372-b17d-c153-73ad-4cd8b6c49758@gmail.com>
Hello,
I think that the paper "Two-Level Type Theory and Applications"
(https://arxiv.org/abs/1705.03307), whose last version has been
submitted on arXiv last month, answers these questions. One of the
intended models of 2LTT is the presheaf category Ĉ over any model C of
HoTT, and this presheaf model is conservative over C, essentially
because the Yoneda embedding is fully faithful. This means that we can
always work in 2LTT instead of HoTT.
Rafaël
On 1/7/20 8:59 PM, Kristina Sojakova wrote:
> Dear all,
>
> I have been increasingly running into situations where I wished I had
> an extensional equality type with a reflection rule in HoTT, in
> addition to the intensional one to which univalence pertains. I know
> that type systems with two equalities have been studied in the HoTT
> community (e.g., VV's HTS), but last time I discussed this with people
> it seemed the situation was not yet well-understood. So my question
> is, what exactly goes wrong if we endow HoTT with an extensional type?
>
> Thank you,
>
> Kristina
>
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next prev parent reply other threads:[~2020-01-07 22:03 UTC|newest]
Thread overview: 5+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-01-07 19:59 Kristina Sojakova
2020-01-07 22:03 ` Rafaël Bocquet [this message]
2020-01-07 22:11 ` Kristina Sojakova
2020-01-07 22:18 ` Rafaël Bocquet
[not found] ` <CALCpNBoWKXbQgdJ2Pqq_G7J_0D48OVGUeQoBnOfDHzC__GWkHA@mail.gmail.com>
2020-01-07 23:26 ` Kristina Sojakova
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