From: Nicolai Kraus <nicola...@gmail.com>
To: Michael Shulman <shu...@sandiego.edu>
Cc: Ulrik Buchholtz <ulrikbu...@gmail.com>,
Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Identity versus equality
Date: Sun, 10 May 2020 15:27:17 +0100 [thread overview]
Message-ID: <CA+AZBBovtP9H9rLhZOFio2dj+83uYvwmb9dd76JrMGM3gz30sQ@mail.gmail.com> (raw)
In-Reply-To: <CAOvivQwAeSU2f8Z6c8aMDDwAgryKNjVYGF+pu5PDBuYVr=Hkvg@mail.gmail.com>
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On Sun, May 10, 2020 at 3:01 PM Michael Shulman <shu...@sandiego.edu>
wrote:
> On Sun, May 10, 2020 at 5:53 AM Ulrik Buchholtz
> <ulrikbu...@gmail.com> wrote:
> > The 2-level type theories can be viewed as another way of making a type
> theory that is faithful to the idea that everything is based on sets.
>
> While I kind of see how one could say this, I think it's misleading
> especially in light of the above dichotomy, becuase 2LTT doesn't imply
> any of the *internal* "types are based on sets" axioms for the fibrant
> layer. As you know, 2LTT without additional axioms is conservative
> over HoTT, while even with stronger axioms it can still be modeled in
> many or all higher toposes.
>
I agree with Mike - sorry Ulrik :-)
For me, "everything is based on sets" would mean that every fibrant type
can be written as the realization of a (semi-) simplicial type, or
something like this.
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next prev parent reply other threads:[~2020-05-10 14:27 UTC|newest]
Thread overview: 61+ messages / expand[flat|nested] mbox.gz Atom feed top
2020-05-05 8:47 Ansten Mørch Klev
2020-05-06 16:02 ` [HoTT] " Joyal, André
2020-05-06 19:01 ` Steve Awodey
2020-05-06 19:18 ` Michael Shulman
2020-05-06 19:31 ` Steve Awodey
2020-05-06 20:30 ` Joyal, André
2020-05-06 22:52 ` Thorsten Altenkirch
2020-05-06 22:54 ` Thorsten Altenkirch
2020-05-06 23:29 ` Joyal, André
2020-05-07 6:11 ` Egbert Rijke
2020-05-07 6:58 ` Thorsten Altenkirch
2020-05-07 9:04 ` Ansten Mørch Klev
2020-05-07 10:09 ` Thomas Streicher
2020-05-07 16:13 ` Joyal, André
2020-05-07 21:41 ` David Roberts
2020-05-07 23:43 ` Joyal, André
2020-05-07 23:56 ` David Roberts
2020-05-08 6:40 ` Thomas Streicher
2020-05-08 21:06 ` Joyal, André
2020-05-08 23:44 ` Steve Awodey
2020-05-09 2:46 ` Joyal, André
2020-05-09 3:09 ` Jon Sterling
[not found] ` <CADZEZBY+3z6nrRwsx9p-HqYuTxAnwMUHv7JasHy8aoy1oaGPcw@mail.gmail.com>
2020-05-09 2:50 ` Steve Awodey
2020-05-09 8:28 ` Thomas Streicher
2020-05-09 15:53 ` Joyal, André
2020-05-09 18:43 ` Thomas Streicher
2020-05-09 20:18 ` Joyal, André
2020-05-09 21:27 ` Jon Sterling
2020-05-10 2:19 ` Joyal, André
2020-05-10 3:04 ` Jon Sterling
2020-05-10 9:09 ` Thomas Streicher
2020-05-10 11:59 ` Thorsten Altenkirch
2020-05-10 11:46 ` Thorsten Altenkirch
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:20 ` Nicolai Kraus
2020-05-10 14:34 ` Michael Shulman
2020-05-10 14:52 ` Nicolai Kraus
2020-05-10 15:16 ` Michael Shulman
2020-05-10 15:23 ` Nicolai Kraus
2020-05-10 16:13 ` Nicolai Kraus
2020-05-10 16:28 ` Michael Shulman
2020-05-10 18:18 ` Nicolai Kraus
2020-05-10 19:15 ` Thorsten Altenkirch
2020-05-10 19:20 ` Thorsten Altenkirch
2020-05-10 12:53 ` Ulrik Buchholtz
2020-05-10 14:01 ` Michael Shulman
2020-05-10 14:27 ` Nicolai Kraus [this message]
2020-05-10 15:35 ` Ulrik Buchholtz
2020-05-10 16:30 ` Michael Shulman
2020-05-10 18:56 ` Nicolai Kraus
2020-05-10 18:04 ` Joyal, André
2020-05-11 7:33 ` Thomas Streicher
2020-05-11 14:54 ` Joyal, André
2020-05-11 16:37 ` stre...
2020-05-11 16:42 ` Michael Shulman
2020-05-11 17:27 ` Thomas Streicher
2020-05-10 16:51 ` Nicolai Kraus
2020-05-10 18:57 ` Michael Shulman
2020-05-10 19:18 ` Nicolai Kraus
2020-05-10 20:22 ` Michael Shulman
2020-05-10 22:08 ` Joyal, André
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