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

[Joe Hannon]

That paper also has an explanation of the periodic table of categories, including -1-categories and -2-categories, which might give some context to today's discussion of what a -1-type should be. 

As a counterpart to Chris's call for references for some math discussions held today (which must've occurred after I left), as a math student I felt a little out of my depth during some of the more CS-y discussions. Is there some nice reference I could look at for this Howard-Curry theorem? Will that be relevant to our discussions going forward?

Joe

> On Jan 6, 2014, at 17:13, Dmitry Vagner <dmitryvagner at gmail.com> wrote:
> 
> 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)
>>> 
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>> 
>> 
>> 
>> -- 
>> Peng Wang (ÍõÅô)
>> CSAIL, The Stata Center, MIT
>> 77 Massachusetts Ave, 32-G822
>> Cambridge, MA 02139
>> Phone: (617)803-2025
>> Email: wangpeng at csail.mit.edu
>> 
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