From: Michael Shulman <shulman@sandiego.edu>
To: "Kristian Alfsvåg" <kristian.alfsvag@uib.no>
Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] 1-Types are groupoids
Date: Wed, 20 Feb 2019 03:48:39 -0800 [thread overview]
Message-ID: <CAOvivQyMZw-VxY9YbMXa+y+_UTwkF3b-AF=A+xgBTcQh6wzgXA@mail.gmail.com> (raw)
In-Reply-To: <591a0ad8-cafb-41a2-8353-c8e389c64a32@googlegroups.com>
I assume you mean a proof inside of type theory? This is Exercise 9.6
in the book; I don't know offhand of anywhere that the proof is
written out. You do need to assume the groupoids are
saturated/univalent ("groupoids" in the terminology of the book rather
than "pregroupoids").
On Wed, Feb 20, 2019 at 3:08 AM <kristian.alfsvag@uib.no> wrote:
>
> Hi
>
> I was wondering whether there exists a proof in literature that the type of 1-truncated types is equivalent to the type of groupoids (defined as categories with only isomorphisms, for example).
>
> I.e. a truncated version of the "types as infinity categories" viewpoint.
>
> Thanks in advance,
> Kristian Alfsvåg
>
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next prev parent reply other threads:[~2019-02-20 11:48 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-02-20 11:08 kristian.alfsvag
2019-02-20 11:48 ` Michael Shulman [this message]
2019-02-20 12:05 ` Niels van der Weide
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