From: Jon Sterling <jon@jonmsterling.com>
To: "David Wärn" <codwarn@gmail.com>
Cc: homotopytypetheory@googlegroups.com
Subject: Re: [HoTT] Free higher groups
Date: Fri, 21 Apr 2023 20:30:39 +0200 [thread overview]
Message-ID: <D102F774-D134-46B9-A70A-51CB84BE4B6F@jonmsterling.com> (raw)
In-Reply-To: <f2af459c-53a6-e7b9-77db-5cbf56da17f3@gmail.com>
Dear David,
Congratulations on your beautiful result; I'm looking forward to understanding the details. Recently I had been wondering if anyone had proved this, and I am delighted to see that it is now done.
Best wishes,
Jon
On 21 Apr 2023, at 12:04, David Wärn wrote:
> Dear all,
>
> I'm happy to announce a solution to one of the oldest open problems in synthetic homotopy theory: the free higher group on a set is a set.
>
> The proof proceeds by describing path types of pushouts as sequential colimits of pushouts, much like the James construction. This description should be useful also in many other applications. For example it gives a straightforward proof of Blakers-Massey.
>
> Best wishes,
> David
>
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next prev parent reply other threads:[~2023-04-21 18:30 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
[not found] <AQHZesxzxECCXAdlIUadD6wxcH+RXA==>
2023-04-21 10:04 ` David Wärn
2023-04-21 11:28 ` [HoTT] " Ulrik Buchholtz
2023-04-21 14:32 ` [HoTT] " Peter LeFanu Lumsdaine
2023-04-21 18:30 ` Jon Sterling [this message]
2023-04-22 0:24 ` Nicolai Kraus
2023-04-25 0:02 ` Michael Shulman
2023-04-25 0:37 ` Dan Christensen
2023-04-28 17:59 ` Michael Shulman
2023-04-29 17:37 ` Dan Christensen
2023-04-29 18:37 ` Steve Awodey
2023-04-29 18:49 ` Ulrik Buchholtz
2023-04-29 19:22 ` Steve Awodey
2023-04-30 0:43 ` Michael Shulman
2023-04-29 18:57 ` Dan Christensen
2023-04-29 19:06 ` Jasper Hugunin
2023-05-02 8:35 ` 'Thorsten Altenkirch' via Homotopy Type Theory
2023-05-02 8:48 ` 'Thorsten Altenkirch' via Homotopy Type Theory
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