Discussion of Homotopy Type Theory and Univalent Foundations
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From: Ali Caglayan <alizter@gmail.com>
To: Homotopy Type Theory <HomotopyTypeTheory@googlegroups.com>
Subject: [HoTT] Re: Weaker Freudenthal
Date: Sun, 4 Aug 2019 03:43:41 -0700 (PDT)	[thread overview]
Message-ID: <a4549eab-f563-42ad-a95a-10166e8e0664@googlegroups.com> (raw)
In-Reply-To: <81b245ba-e70f-4a13-8d0c-4eaad69f3da8@googlegroups.com>

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Here is an observation I had made:

We have that A is k-connected, we can show that susp A is (k+1)-connected 
and then show that loop susp A is k-connected. This gives us a k-connected 
map A -> 1 and a k-connected map loop susp A -> 1. This gives us a diagram 
which commutes with A and loop susp A in the top corners and 1 in the 
bottom. The LHS composition is homotopic to the RHS composition hence 
naming eta : A -> loop susp A, we have eta o unitmap being k-connected 
hence eta must also be k-connected. This isn't quite there.

Now I was hoping to use the fact that loop spaces are pullbacks hence there 
are maps coming out of 1s hence (k+1)-connectedness appears, but I couldn't 
get it to work.

On Sunday, 4 August 2019 12:59:09 UTC+3, Ali Caglayan wrote:
> Can we prove that the map A -> loop susp A is (k+1)-connected for a 
> k-connected A, without having to invoke Freudenthal?

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      reply	other threads:[~2019-08-04 10:43 UTC|newest]

Thread overview: 2+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2019-08-04  9:59 [HoTT] " Ali Caglayan
2019-08-04 10:43 ` Ali Caglayan [this message]

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