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
> > 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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