My Math Forum Homotopy hypothesis

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 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 infinity-groupoids 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: 1,922 Thanks: 534 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. Thanks from zambod Last edited by Maschke; March 24th, 2017 at 08:49 AM.
 March 24th, 2017, 10:26 AM #3 Senior Member   Joined: Aug 2012 Posts: 1,922 Thanks: 534 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, n-categories (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? Thanks from zambod
March 24th, 2017, 08:55 PM   #4
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 Originally Posted by Maschke OP, can you say why you asked this question? Are you a postdoc? Or is this something you just ran across online?
I'm in tech, not math proper. I've worked using dependent type theory. I'm trying to understand the mathematical background of homotopy type theory: https://homotopytypetheory.org/

March 24th, 2017, 10:06 PM   #5
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 Originally Posted by zambod I'm in tech, not math proper. I've worked using dependent type theory. I'm trying to understand the mathematical background of homotopy type theory: https://homotopytypetheory.org/
I know who Voevodsky and the bare basics of HoTT but not much more. I know what a homotopy is anyway. I gather this is related somehow to intuitionist type theory, in which they deny the law of the excluded middle but manage to recover most of modern math anyway.

I used to read John Baez's This Weeks Finds articles which is where I heard about n-categories. And I've seen a little category theory in the context of abstract algebra. That's about it for me.

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