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? > > > > -- > > You received this message because you are subscribed to the Google > Groups "Homotopy Type Theory" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to HomotopyTypeTheory+unsubscribe@googlegroups.com . > > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. For more options, visit https://groups.google.com/d/optout.