From: Michael Shulman <shulman@sandiego.edu>
To: Brian Sanderson <brianjsanderson@gmail.com>
Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Homotopy type of simply connected spaces.
Date: Thu, 10 Jan 2019 13:11:58 -0800 [thread overview]
Message-ID: <CAOvivQxzLoy=574snuvrv4x5+wOsnXKoeR=DOi_F84r=nGapoQ@mail.gmail.com> (raw)
In-Reply-To: <fd7763e9-4110-4933-9638-683aa4b83a85@googlegroups.com>
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
<brianjsanderson@gmail.com> wrote:
>
> 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:[~2019-01-10 21:12 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 [this message]
2019-01-11 11:49 ` Brian Sanderson
2019-01-11 12:01 ` Cory Knapp
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