From: Brian Sanderson <firstname.lastname@example.org>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Homotopy type of simply connected spaces.
Date: Fri, 11 Jan 2019 03:49:06 -0800 (PST) [thread overview]
Message-ID: <email@example.com> (raw)
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Thanks for the references. So am I allowed to say a type is simply
connected if any two paths are equal, or is that a meta statement which has
no meaning within type theory.
On Thursday, 10 January 2019 21:12:13 UTC, Michael Shulman wrote:
> Yes, you have to truncate the equality. See section 7.5 of the HoTT
> Book, and also Exercise 7.6.
> On Thu, Jan 10, 2019 at 12:36 PM Brian Sanderson
> > The type of a simply connected space would seem to make it just a set as
> any two paths with the same endpoints would be homotopic. I see that there
> would not be a continuous function from the space of pairs of paths to
> homotopies between them. What would the type of a simply connected space
> look like? Can I say in type theory any two equalities are equal without
> having a function?
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next prev parent reply other threads:[~2019-01-11 11:49 UTC|newest]
Thread overview: 4+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-01-10 20:36 Brian Sanderson
2019-01-10 21:11 ` Michael Shulman
2019-01-11 11:49 ` Brian Sanderson [this message]
2019-01-11 12:01 ` Cory Knapp
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