Re: [HoTT] Homotopy type of simply connected spaces.

[Brian Sanderson <brianjsanderson@gmail.com>]

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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 
> <brianjs...@gmail.com <javascript:>> 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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