*[HoTT] Weaker Freudenthal@ 2019-08-04 9:59 Ali Caglayan2019-08-04 10:43 ` [HoTT] " Ali Caglayan 0 siblings, 1 reply; 2+ messages in thread From: Ali Caglayan @ 2019-08-04 9:59 UTC (permalink / raw) To: Homotopy Type Theory [-- Attachment #1.1: Type: text/plain, Size: 514 bytes --] Can we prove that the map A -> loop susp A is (k+1)-connected for a k-connected A, without having to invoke Freudenthal? -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/81b245ba-e70f-4a13-8d0c-4eaad69f3da8%40googlegroups.com. [-- Attachment #1.2: Type: text/html, Size: 945 bytes --] ^ permalink raw reply [flat|nested] 2+ messages in thread

*[HoTT] Re: Weaker Freudenthal2019-08-04 9:59 [HoTT] Weaker Freudenthal Ali Caglayan@ 2019-08-04 10:43 ` " Ali Caglayan0 siblings, 0 replies; 2+ messages in thread From: Ali Caglayan @ 2019-08-04 10:43 UTC (permalink / raw) To: Homotopy Type Theory [-- Attachment #1.1: Type: text/plain, Size: 1292 bytes --] 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? > -- You received this message because you are subscribed to the Google Groups "Homotopy Type Theory" group. To unsubscribe from this group and stop receiving emails from it, send an email to HomotopyTypeTheory+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/HomotopyTypeTheory/a4549eab-f563-42ad-a95a-10166e8e0664%40googlegroups.com. [-- Attachment #1.2: Type: text/html, Size: 1862 bytes --] ^ permalink raw reply [flat|nested] 2+ messages in thread

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