Timeline for Non-unique splittings of homotopy idempotents
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 16, 2014 at 11:31 | comment | added | Mike Shulman | If I had to pick where to look for a problem, I'd probably start with the assertion that we only need to fill one 5-simplex and all the other coherence comes for free. I'd probably go back to the definition of coherent idempotent in HTT and see how many simplices will actually need to be added. | |
| Dec 12, 2014 at 23:13 | comment | added | Will Sawin | @MikeShulman What part of the argument are you most skeptical of? Perhaps precisely identifying the problem here will help prove or disprove the claim in general. | |
| Dec 12, 2014 at 6:02 | comment | added | Mike Shulman | Hmm. I'm not sure about the argument, but as in your last paragraph I'm pretty sure this can't happen with an identity map. Per HTT, the space of coherent idempotents is equivalent to the space of retractions, so the space of coherentifications of a homotopy idempotent should be equivalent to the space of its splittings (that induce the specified witness of idempotence $f\circ f \sim f$). But if $f$ is the identity with its canonical witness, then the latter space is equivalent to the space of "spaces equipped with an equivalence to $X$", and hence is contractible. | |
| Dec 12, 2014 at 4:38 | history | answered | Will Sawin | CC BY-SA 3.0 |