Discussion of Homotopy Type Theory and Univalent Foundations
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From: "'Urs Schreiber' via Homotopy Type Theory" <HomotopyTypeTheory@googlegroups.com>
To: Michael Shulman <shulman@sandiego.edu>
Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] What is knot in HOTT?
Date: Fri, 20 Jul 2018 20:42:10 +0400
Message-ID: <CA+KbugdyCk+3yqUthkuKK31idy2BsYFrEBDJyTWAkQ9Vu+EGTQ@mail.gmail.com> (raw)
In-Reply-To: <CA+KbugdpHcNpOYz2r3tog=PqZ_mW+rL8DA8AEP=zL_fcFmxfJg@mail.gmail.com>

Gr, here I mean "flat" where I wrote "Disc", and the counit should go
the other way around...

On 7/20/18, Urs Schreiber <urs.schreiber@googlemail.com> wrote:
>> It seems to me that especially if we want to construct *particular*
>> knots, we would need the smooth reals to at least be a ring and
>> probably to support trigonometric functions.
>
> One could require an isomorphism
>
>  Disc(A) = R_{Cauchy}
>
> such that combined with the counit
>
>  A --> Disc(A) = R_Cauchy
>
> this respects the homogeneous type structure on both sides (i.e the
> postulated one on the left, the canonical one given by addition on the
> right).
>
> To test such choices of axioms, it would be very helpful to have a
> concrete proposition in knot theory in mind, which one could aim for.
> Preferably some very simple proposition which is still of interest.
>
> Best,
> urs
>

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  reply index

Thread overview: 16+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2018-07-19  5:18 José Manuel Rodriguez Caballero
2018-07-19  5:45 ` Egbert Rijke
2018-07-19  8:55   ` Ali Caglayan
2018-07-19 15:31     ` Michael Shulman
2018-07-20 10:27       ` 'Urs Schreiber' via Homotopy Type Theory
2018-07-20 13:32         ` Michael Shulman
2018-07-20 13:45           ` 'Urs Schreiber' via Homotopy Type Theory
2018-07-20 14:54             ` Michael Shulman
2018-07-20 15:17               ` Joyal, André
2018-07-20 16:40               ` 'Urs Schreiber' via Homotopy Type Theory
2018-07-20 16:42                 ` 'Urs Schreiber' via Homotopy Type Theory [this message]
2019-11-20 19:13     ` Ali Caglayan
2019-11-20 21:02       ` andré hirschowitz
2018-07-19 17:56   ` Daniel R. Grayson
2018-07-19 18:38     ` Egbert Rijke
2018-07-19 20:07       ` José Manuel Rodriguez Caballero

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Discussion of Homotopy Type Theory and Univalent Foundations

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