From: Michael Shulman <shu...@sandiego.edu>
To: Thorsten Altenkirch <Thorsten....@nottingham.ac.uk>
Cc: Jon Sterling <j...@jonmsterling.com>,
"'Martin Escardo' via Homotopy Type Theory"
<homotopyt...@googlegroups.com>
Subject: Re: [HoTT] Identity versus equality
Date: Sun, 10 May 2020 07:01:51 -0700 [thread overview]
Message-ID: <CAOvivQxD-gJgp=Az0b=ysOygQryp695uNQjKbrOr-cEQTU-aeA@mail.gmail.com> (raw)
In-Reply-To: <154D1B4B-6881-4269-8BA1-1CE8EBB0BE0D@nottingham.ac.uk>
On Sun, May 10, 2020 at 4:46 AM Thorsten Altenkirch
<Thorsten....@nottingham.ac.uk> wrote:
> Defining simplicial types isn't entirely straightforward (as you know I suppose), because Delta is not directed. We can do semi-simplicial types as a Reedy limit, i.e. an infinite Sigma type
We can certainly *talk* about simplicial types in 2LTT as exofunctors
from the exocategory Delta to the exocategory Type. I assume the
point you're making is that we don't have a (fibrant) *type of*
simplicial types, whereas we do have a fibrant type of semisimplicial
types (under appropriate axioms)?
> You need some extra principles, e.g. that strict Nat is fibrant or maybe better that certain coinductive types exist.
Personally, I think the best axiom to use here is that exo-Nat is
*cofibrant*, i.e. Pi-types with domain exo-Nat preserve fibrancy. We
don't know how to model "exo-Nat is fibrant" in all higher toposes,
but it's easy to interpret "exo-Nat is cofibrant" in such models,
since Pi-types with domain exo-Nat are just externally-infinite
products.
next prev parent reply other threads:[~2020-05-10 14:02 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 [this message]
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
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
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to='CAOvivQxD-gJgp=Az0b=ysOygQryp695uNQjKbrOr-cEQTU-aeA@mail.gmail.com' \
--to="shu..."@sandiego.edu \
--cc="Thorsten...."@nottingham.ac.uk \
--cc="homotopyt..."@googlegroups.com \
--cc="j..."@jonmsterling.com \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).