From: Cory Knapp <cory.m.knapp@gmail.com>
To: Brian Sanderson <brianjsanderson@gmail.com>
Cc: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: Re: [HoTT] Homotopy type of simply connected spaces.
Date: Fri, 11 Jan 2019 12:01:58 +0000 [thread overview]
Message-ID: <CADzYOhfK8CUMaeQV_BqBQdkmCz71ucPpWHUCV_1v8uEC-TiV=Q@mail.gmail.com> (raw)
In-Reply-To: <d2f00740-1c9c-47a2-b731-c8276ceaebd7@googlegroups.com>
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Using the language of the hott book, a type is simply connected if there
*merely exists* a homotopy between any two paths.
On Fri, Jan 11, 2019, 11:49 Brian Sanderson <brianjsanderson@gmail.com>
wrote:
> 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
>> <brianjs...@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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prev parent reply other threads:[~2019-01-11 12:02 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
2019-01-11 12:01 ` Cory Knapp [this message]
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