From: Michael Shulman <shu...@sandiego.edu>
To: du yu <doof...@gmail.com>
Cc: Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] The Interval type in Hott vs. in real analysis
Date: Tue, 17 Oct 2017 13:40:23 -0700 [thread overview]
Message-ID: <CAOvivQydiv9Q1ctierSksVrOEr5gp+VnWJB_8p6BiQ2ZqJCLqQ@mail.gmail.com> (raw)
In-Reply-To: <bc6ceb84-9d61-4c35-9179-d688803fd110@googlegroups.com>
The higher inductive "homotopical" interval is a very different thing
from the "topological" interval of real numbers. The connection is
that the homotopical interval is the "shape" or "fundamental
infinity-groupoid" of the topological interval. The tradition in
homotopy theory of identifying topological spaces with their shapes,
or differently-put of studying infinity-groupoids indirectly by way of
topological spaces whose shapes they are, leads to the confusion and
the coincidence of names.
On Tue, Oct 17, 2017 at 9:39 AM, du yu <doof...@gmail.com> wrote:
> I have seen the definition of Interval type [0,1] in HoTT book as higher
> inductive type and in cubical type theory as De-morgan algebra, and in real
> analysis there exists continuous function from [0,1] to Real,which means
> [0,1] is equivalent to R . How are these thing relate to each other?
>
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prev parent reply other threads:[~2017-10-17 20:40 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-10-17 16:39 du yu
2017-10-17 20:40 ` Michael Shulman [this message]
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