Timeline for On triangulated categories of pro-objects
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jul 14, 2015 at 23:30 | comment | added | Ilan Barnea | In this paper we also define the pro-category of an arbitrary locally small $\infty$-category and prove that the Yoneda embedding is fully faithful. I assume it will not be to hard to show also the other claims you've made. | |
| Jul 14, 2015 at 23:20 | comment | added | Ilan Barnea | Your claim that if $M$ is a proper model category with underlying $\infty$-category $\tilde M$ and $Pro(M)$ is equipped with Isaksen's strict model structure, then the underlying $\infty$-category of $Pro(M)$ is $Pro(\tilde M)$ is shown in the following paper arxiv.org/abs/1507.01564 | |
| Nov 15, 2013 at 16:49 | comment | added | Marc Hoyois | Prop. 7.1.12 in Hovey's book says that the derived functor of a Quillen functor between stable model categories is always exact (for the induced triangulated structures). | |
| Oct 30, 2013 at 21:50 | comment | added | Mikhail Bondarko | Could you give a more precise reference to Hovey? | |
| Sep 21, 2013 at 2:44 | comment | added | Marc Hoyois | Actually, I guess it's possible to prove all this using Isaksen's model structure. I first thought of using $\infty$-categories because model categories don't make it easy to prove that a left Quillen functor preserves finite homotopy limits, but in fact when it's between stable model categories it's automatic (this is in Hovey). | |
| Sep 20, 2013 at 18:54 | comment | added | Mikhail Bondarko | So, you think that $\infty$-categories are appropriate here? Thank you!! Yet all of this is somewhat confusing.:) | |
| Sep 20, 2013 at 18:04 | history | answered | Marc Hoyois | CC BY-SA 3.0 |