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 20:40:56 +0400 [thread overview]
Message-ID: <CA+KbugdpHcNpOYz2r3tog=PqZ_mW+rL8DA8AEP=zL_fcFmxfJg@mail.gmail.com> (raw)
In-Reply-To: <CAOvivQyz+Vy7TCzSWhE8d9MEkWn5Vcuh1rNb8hxs=h=N=LwtnA@mail.gmail.com>
> 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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next prev parent reply other threads:[~2018-07-20 16:40 UTC|newest]
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 [this message]
2018-07-20 16:42 ` 'Urs Schreiber' via Homotopy Type Theory
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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