From: Michael Shulman <shulman@sandiego.edu>
To: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
Cc: Thorsten Altenkirch <Thorsten.Altenkirch@nottingham.ac.uk>,
Ulrik Buchholtz <ulrikbuchholtz@gmail.com>,
homotopytypetheory@googlegroups.com
Subject: Re: [HoTT] Re: Precategories, Categories and Univalent categories
Date: Thu, 8 Nov 2018 06:38:44 -0800 [thread overview]
Message-ID: <CAOvivQyLvtP9uEPbu+06s79dLzvTKkju-h3ctcxoyjigkb7U9Q@mail.gmail.com> (raw)
In-Reply-To: <20181108115815.GA5022@mathematik.tu-darmstadt.de>
Actually, you don't need strict equality on categories to talk about
strict Grothendieck fibrations in type theory:
https://ncatlab.org/nlab/show/displayed+category
On Thu, Nov 8, 2018 at 3:58 AM Thomas Streicher
<streicher@mathematik.tu-darmstadt.de> wrote:
>
> Thorsten asked why I prefer to have strict equality on categories.
> The answer is that one needs it in category theory typically when
> speaking about Grothendieck fibrations.
> And the latter is most useful in many contexts in particular when
> understanding geometric morphisms. This by the way also extends to
> Grothendieck fibrations in quasicategories as in Joyal and Lurie's
> accounts.
>
> Thomas
>
>
> --
> You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
> For more options, visit https://groups.google.com/d/optout.
--
You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group.
To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com.
For more options, visit https://groups.google.com/d/optout.
next prev parent reply other threads:[~2018-11-08 14:39 UTC|newest]
Thread overview: 46+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-11-07 10:03 [HoTT] " Ali Caglayan
2018-11-07 10:31 ` [HoTT] " Paolo Capriotti
2018-11-07 10:35 ` Ulrik Buchholtz
2018-11-07 10:37 ` Ulrik Buchholtz
2018-11-07 11:09 ` Peter LeFanu Lumsdaine
2018-11-07 11:43 ` Ulrik Buchholtz
2018-11-07 11:50 ` Erik Palmgren
2018-11-07 11:51 ` Ulrik Buchholtz
2018-11-07 12:03 ` Erik Palmgren
2018-11-07 12:21 ` Martín Hötzel Escardó
2018-11-07 13:00 ` Erik Palmgren
2018-11-07 13:02 ` Bas Spitters
2018-11-07 13:47 ` Ali Caglayan
2018-11-07 13:53 ` Thomas Streicher
2018-11-07 14:05 ` Thorsten Altenkirch
2018-11-07 13:58 ` Thorsten Altenkirch
2018-11-07 14:14 ` Ulrik Buchholtz
2018-11-07 14:27 ` Peter LeFanu Lumsdaine
[not found] ` <CAOvivQyG1q9=3YoS8hX3bRQK0yi+mpBnJu+rqb3oon0uPLpZ4A@mail.gmail.com>
2018-11-07 20:01 ` Michael Shulman
2018-11-08 21:37 ` Martín Hötzel Escardó
2018-11-08 21:43 ` Michael Shulman
2018-11-09 4:43 ` Andrew Polonsky
2018-11-09 10:18 ` Ulrik Buchholtz
2018-11-09 10:57 ` Paolo Capriotti
2018-11-07 14:31 ` Thorsten Altenkirch
2018-11-07 14:05 ` Peter LeFanu Lumsdaine
2018-11-07 14:28 ` Ulrik Buchholtz
2018-11-07 15:35 ` Thomas Streicher
2018-11-07 16:54 ` Thorsten Altenkirch
2018-11-07 16:56 ` Thorsten Altenkirch
2018-11-07 17:31 ` Eric Finster
2018-11-08 11:58 ` Thomas Streicher
2018-11-08 12:23 ` [HoTT] " Emily Riehl
2018-11-08 12:28 ` Emily Riehl
2018-11-08 14:01 ` Thomas Streicher
2018-11-08 16:10 ` Thomas Streicher
2018-11-08 14:38 ` Michael Shulman [this message]
2018-11-08 21:08 ` [HoTT] " Thomas Streicher
2018-11-08 21:30 ` Michael Shulman
2018-11-09 11:56 ` Thomas Streicher
2018-11-09 13:46 ` Michael Shulman
2018-11-09 15:06 ` Thomas Streicher
2018-11-08 16:01 ` Thorsten Altenkirch
2018-11-08 19:39 ` Thorsten Altenkirch
2018-11-07 20:00 ` Michael Shulman
2018-11-08 21:35 ` Martín Hötzel Escardó
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=CAOvivQyLvtP9uEPbu+06s79dLzvTKkju-h3ctcxoyjigkb7U9Q@mail.gmail.com \
--to=shulman@sandiego.edu \
--cc=Thorsten.Altenkirch@nottingham.ac.uk \
--cc=homotopytypetheory@googlegroups.com \
--cc=streicher@mathematik.tu-darmstadt.de \
--cc=ulrikbuchholtz@gmail.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).