March 24th, 2017, 06:43 AM  #1 
Newbie Joined: Mar 2016 From: Alabama Posts: 18 Thanks: 0  Homotopy hypothesis
What are the considerations bearing on the conjecture that infinitygroupoids are spaces? Do you consider it likely or unlikely? What do most mathematicians think?

March 24th, 2017, 08:45 AM  #2 
Senior Member Joined: Aug 2012 Posts: 1,521 Thanks: 364 
Why don't you outline what that is, what it means, why it's important, what conclusions you've come to, and where you are stuck in your understanding? Your question is above the level of the typical question here, and I'm sure many of us, myself included, would appreciate a refresher or an introduction to the terminology. Last edited by Maschke; March 24th, 2017 at 08:49 AM. 
March 24th, 2017, 10:26 AM  #3 
Senior Member Joined: Aug 2012 Posts: 1,521 Thanks: 364 
PS  John Baez has a "simplfied" explanation here ...http://math.ucr.edu/home/baez/homotopy/homotopy.pdf Unfortunately it's not simple enough for me. You need to know category theory, ncategories (categories of categories of categories ...), algebraic topology, and a lot of other heavy duty math. The level of the material is at the advanced Ph.D. student (working on thesis) or postdoc. OP, can you say why you asked this question? Are you a postdoc? Or is this something you just ran across online? 
March 24th, 2017, 08:55 PM  #4  
Newbie Joined: Mar 2016 From: Alabama Posts: 18 Thanks: 0  Quote:
 
March 24th, 2017, 10:06 PM  #5  
Senior Member Joined: Aug 2012 Posts: 1,521 Thanks: 364  Quote:
I used to read John Baez's This Weeks Finds articles which is where I heard about ncategories. And I've seen a little category theory in the context of abstract algebra. That's about it for me.  

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