[HoTT-reading-group] Today; Next Monday

[Gregory Malecha]

Despite getting a little bit derailed at the end of yesterday, I found the
discussion to be very useful. In particular, being a type theorist I don't
get the mathematical point of view just from reading the book. I'm happy to
offer the 'type theorist perspective' whenever it is useful but I feel that
those intuitions are shallower (because they are less interested in the
model and more interested in doing things above the model) than the
mathematical ones.

I'm enjoying it, and thanks for the example, Jason. There is still
something that feels strange about it, but I will continue to wrapping my
head around it.


On Mon, Feb 17, 2014 at 11:42 PM, Jason Gross <jasongross9 at gmail.com> wrote:

> Next week, I plan for us to do what was actually on the schedule for this
> week, namely covering questions on chapters 3 and 4 and reviewing exercises
> 3.13, 3.14, and 4.5; please come in with the exercises completed or with
> questions about how to do them.
>
> I also welcome advice and feedback on the reading group (now or in the
> future, in person, or by private email), whether that's "I want to get
> *foo* out of the group, and I'm not getting it" or "keep doing what
> you're doing" or "more/fewer exercises" or something else.
>
> Finally, today in the HoTT reading group, we talked about how chapter 4
> seems dry to those with no prior knowledge of how the various definitions
> of equivalence are used in math, but interesting to those who can connect
> them up to various other bits of math; we talked about various notions of
> contractibility (inhabited hprop; equivalent to unit; filling of
> spheres/holes); a bit about truncation; and I brought up the fact that The
> Truncation Map |_| : ℕ -> ‖ℕ‖ is nearly Invertible<http://homotopytypetheory.org/2013/10/28/the-truncation-map-_-%E2%84%95-%E2%80%96%E2%84%95%E2%80%96-is-nearly-invertible/>,
> which was perhaps a mistake, given that I botched the presentation.  I will
> leave it up to those interested to read the blog post<http://homotopytypetheory.org/2013/10/28/the-truncation-map-_-%E2%84%95-%E2%80%96%E2%84%95%E2%80%96-is-nearly-invertible/>,
> Nicolai's Agda code<http://red.cs.nott.ac.uk/~ngk/html-trunc-inverse/trunc-inverse.html>,
> or my own Coq version of it <https://gist.github.com/JasonGross/9064514>.
>  I think the essence of it is that you can extract information even from
> contractible types, which I show in a much shorter Coq example<https://gist.github.com/JasonGross/9064636> involving
> Bool, and two values [x] and [y] where we have [x = y] but we have a
> (dependent) function [f] with [f x ≠ f y].  (I believe this is related to
> the difference between having a path between two points in a fiber, and a
> path between those points which lies over the constant path, and how you
> can have the former without the latter.)
>
> -Jason
>
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>


-- 
gregory malecha
http://www.people.fas.harvard.edu/~gmalecha/
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