From: Michael Shulman <shulman@sandiego.edu>
To: Steve Awodey <steveawodey@gmail.com>
Cc: Ulrik Buchholtz <ulrikbuchholtz@gmail.com>,
Dan Christensen <jdc@uwo.ca>,
"homotopytypetheory@googlegroups.com"
<homotopytypetheory@googlegroups.com>
Subject: Re: [HoTT] Free higher groups
Date: Sat, 29 Apr 2023 17:43:15 -0700 [thread overview]
Message-ID: <CADYavpzinvAW_PgLUPbp4NyykJxhEbmBsQSC6rQroZWCcFg9xw@mail.gmail.com> (raw)
In-Reply-To: <5D0912E6-075B-47EE-87B8-8B5118DDF07C@gmail.com>
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Bringing this thread back to David's original announcement of his new
result, one thing that intrigues me about it is that proceeds by
constructing successive approximations to the desired path space and then
taking a sequential colimit. This reminds me of some other sequential
constructions that also achieved surprising (to me) things, like Egbert's
join construction for building propositional truncation out of nonrecursive
HITs, and the splitting of a quasi-idempotent by a sequential (co)limit
that Lurie used in higher category theory and I then adapted to HoTT. I
wonder if there are other surprising applications of this principle.
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next prev parent reply other threads:[~2023-04-30 0:43 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
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 [this message]
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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