Timeline for Euclidean model structure on multipointed $d$-spaces
Current License: CC BY-SA 4.0
9 events
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| May 15, 2018 at 7:39 | comment | added | Philippe Gaucher | @TimCampion The model category constructed in my paper "A model category for the homotopy theory of concurrency" on the category of flows (which are morally speaking multipointed $d$-spaces without underlying topological space) is left determined too. This can be proved also by using Mark Olschok's argument. | |
| May 15, 2018 at 7:33 | comment | added | Philippe Gaucher | @TimCampion The Quillen model structure on $\mathrm{Top}$ is left determined. This result is due to Mark Olschok. By adapting his argument, I can prove that the model structure with the $\mathrm{Glob}$ is left determined as well. The result is not in the paper I mentioned, maybe I'll write a short note about that one day. | |
| May 14, 2018 at 14:20 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| May 14, 2018 at 14:16 | comment | added | Tim Campion | I think in order to hit upon a good cylinder, I would need to learn something about what this model category is modeling, and look for an object playing the role of "the walking isomorphism". @DavidWhite certainly most of the conditions still use large-cardinal axioms which are known to be unprovable in ZFC (unless ZFC is inconsistent). But the second paper does have some results in ZFC under strong definability hypotheses. But I agree, this probably isn't the most fruitful direction to look in. | |
| May 14, 2018 at 14:10 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| May 14, 2018 at 10:05 | comment | added | Philippe Gaucher | I am 100% (well 99.99%) sure that there is no need of any large cardinal axiom because it is a purely geometric problem on a very specific category. If I could at least have a geometric intuition of what the cylinder could be... The cylinder can be found by the usual functorial factorization of the codiagonal map of course but that does not help very much. By asking this question, I hoped that someone could have a geometric intuition which could be a starting point. | |
| May 14, 2018 at 8:47 | comment | added | David White | The two cited papers with "Bousfield localizations under weaker hypotheses" still use hypotheses not known to be within the scope of classical set theory. So, if Philippe is trying to avoid Vopenka's principle, he'd probably want to avoid those too. Unfortunately, I still don't know how to! | |
| May 14, 2018 at 2:13 | comment | added | Philippe Gaucher | I do use $\Delta$-generated spaces, it is written in the post and therefore all categories are locally presentable. Noone never saw Jeff Smith's argument and some mathematicians I know doubt that he has such an argument. And indeed not all objects are cofibrant, So Olschok's theory cannot be applied. It is a different configuration. | |
| May 13, 2018 at 20:04 | history | answered | Tim Campion | CC BY-SA 4.0 |