Discussion of Homotopy Type Theory and Univalent Foundations
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From: Chris Kapulkin <k.kapulkin@gmail.com>
To: HoTT Electronic Seminar Talks
	<hott-electronic-seminar-talks@googlegroups.com>,
	 Homotopy Type Theory <homotopytypetheory@googlegroups.com>,
	categories@mta.ca
Subject: [HoTT] Re: M. Shulman, Towards Third-Generation HOTT, April 14, 21, and 28 - HoTTEST Distinguished Lecture Series
Date: Wed, 13 Apr 2022 21:28:28 -0400	[thread overview]
Message-ID: <CAEXhy3Pjt4=wi5ikinGTqkKXyQKQ6iWOCtyTjz=Bc1zufLz-AQ@mail.gmail.com> (raw)
In-Reply-To: <CAEXhy3MVeK4auqO3MTkjn0JBO0XoqV8k-5RnS=Ofi=VDQv15DA@mail.gmail.com>

The organizers of the HoTT Electronic Seminar Talks are committed to
the diversity and growth of homotopy type theory, and want everybody
to feel comfortable and welcome in our community.

We believe the speaker’s recent statements in the context of the HoTT
Book stand in opposition to these values, and have made the difficult
decision not to hold the upcoming HoTTEST Distinguished Lecture
Series.

Carlo Angiuli
Dan Christensen
Chris Kapulkin

On Mon, Apr 11, 2022 at 9:32 AM Chris Kapulkin <k.kapulkin@gmail.com> wrote:
>
> We are delighted to announce the inaugural HoTTEST Distinguished
> Lecture Series to be given by Mike Shulman (University of San Diego).
> The series consists of three lectures which will take place on April
> 14, 21, and 28 at 11:30 AM Eastern time. The Eastern time zone is now
> observing daylight saving time, making it UTC-04:00.
>
> Each lecture will be one-hour long and will be followed by a 30-minute
> discussion. The title and abstract are below.
>
> The Zoom link is
>
>   https://zoom.us/j/994874377
>
> Further information, including our Google Calendar and Youtube
> channel, is available at
>
>   http://uwo.ca/math/faculty/kapulkin/seminars/hottest.html
>
> We are looking forward to seeing many of you there!
>
> Best wishes,
> Carlo Angiuli
> Dan Christensen
> Chris Kapulkin
>
> *
>
> Mike Shulman
> University of San Diego
>
> Towards Third-Generation HOTT
>
> In Book HoTT, identity is defined uniformly by the principle of
> "indiscernibility of identicals". This automatically gives rise to
> higher structure; but many desired equalities are not definitional,
> and univalence must be asserted by a non-computational axiom. Cubical
> type theories also define identity uniformly, but using paths instead.
> This makes more equalities definitional, and enables a form of
> univalence that computes; but requires inserting all the higher
> structure by hand with Kan operations.
>
> I will present work in progress towards a third kind of homotopy type
> theory, which we call Higher Observational Type Theory (HOTT). In this
> system, identity is not defined uniformly across all types, but
> recursively for each type former: identifications of pairs are pairs
> of identifications, identifications of functions are pointwise
> identifications, and so on. Univalence is then just the instance of
> this principle for the universe. The resulting theory has many useful
> definitional equalities like cubical type theories, but also gives
> rise to higher structure automatically like Book HoTT. Also like Book
> HoTT, it can be interpreted in a class of model categories that
> suffice to present all Grothendieck-Lurie (∞,1)-toposes; and we have
> high hopes that, like cubical type theories, some version of it will
> satisfy canonicity and normalization.
>
> This is joint work with Thorsten Altenkirch and Ambrus Kaposi.

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  reply	other threads:[~2022-04-14  1:28 UTC|newest]

Thread overview: 22+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2022-04-11 13:32 [HoTT] " Chris Kapulkin
2022-04-14  1:28 ` Chris Kapulkin [this message]
2022-04-14  8:32   ` [HoTT] " 'Thorsten Altenkirch' via Homotopy Type Theory
2022-04-14  9:25   ` 'Urs Schreiber' via Homotopy Type Theory
2022-04-14 10:42   ` Thomas Streicher
2022-04-14 11:48   ` Andrej Bauer
2022-04-14 15:49     ` Martín Hötzel Escardó
2022-04-14 20:23   ` Nicolas Alexander Schmidt
2022-04-15  3:00     ` [HoTT] " Alexander Kurz
2022-04-15  9:29       ` Josh Chen
2022-04-15 11:21         ` Ondrej Rypacek
2022-04-15 12:01         ` Martín Hötzel Escardó
2022-04-23 13:03           ` David
2022-04-23 19:36             ` Andreas Nuyts
2022-04-25  9:36               ` David
2022-04-25 16:23                 ` Josh Chen
2022-04-25 19:25                   ` David
2022-04-26  1:18                     ` Josh Chen
2022-04-26  2:04                       ` David
2022-04-26 19:10                         ` Nicolai Kraus
2022-04-27 11:00                           ` Andrej Bauer
2022-04-14 15:49 ` Joyal, André

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