[HoTT-reading-group] Background reading in homotopy theory and higher category theory?

[Dmitry Vagner]

Thank you Jason for the wonderful group and for including us remotely!
Chris, I learned a lot about the homotopy/groupoid/category theory
interface from this amazing expository paper by John Baez:

http://arxiv.org/pdf/math/0608420v2.pdf

For our purposes, section 2 is where all of the interesting (and most
accessible) information is. Only the basic definitions of category theory
(along with your foundational algebraic topology understanding) may be
required to get a lot out of this section. Of particular interest is
section 2.3 - it's on this thing called the "homotopy hypothesis" - which
roughly says that "homotopy n-types are the same as n-groupoids" - taking n
to the limit yields what you are interested in, that from the homotopical
perspective, "topological spaces are the same as (weak)
infinity-groupoids." I feel like this paper does a great job of expositing
these ideas, including what exactly a homotopy n-type is, without much
technical background.

Hope that helps,
Dmitry


On Mon, Jan 6, 2014 at 4:47 PM, Peng Wang <wangp.thu at gmail.com> wrote:

>
>
>
> On Mon, Jan 6, 2014 at 4:41 PM, Chris Jeris <cjeris at gmail.com> wrote:
>
>> First of all, thanks very much to Jason for putting the group together
>> and also making it accessible to us remote participants!
>>
>> I am intrigued by the statement that "infinity-groupoids are the natural
>> models of homotopy theory", but I know little about homotopy theory and
>> nothing about higher category theory.  I have algebraic topology at about
>> the level of Massey's first course (rusty by some years) and basic category
>> theory.  Can anyone suggest some expository works in this area as
>> background or further reading?
>>
>
> Adding to Chris' question, I don't even know about topology or algebraic
> topology, so is there some introductory material on that? (Or is that
> needed?)
>
>>
>> thanks, Chris Jeris (freenode: ystael)
>>
>> _______________________________________________
>> HoTT-reading-group mailing list
>> HoTT-reading-group at mit.edu
>> http://mailman.mit.edu/mailman/listinfo/hott-reading-group
>>
>>
>
>
> --
> Peng Wang (王鹏)
> CSAIL, The Stata Center, MIT
> 77 Massachusetts Ave, 32-G822
> Cambridge, MA 02139
> Phone: (617)803-2025
> Email: wangpeng at csail.mit.edu
>
> _______________________________________________
> HoTT-reading-group mailing list
> HoTT-reading-group at mit.edu
> http://mailman.mit.edu/mailman/listinfo/hott-reading-group
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mailman.mit.edu/pipermail/hott-reading-group/attachments/20140106/174c54f9/attachment.htm