Timeline for Homotopy colimits in subcategories of combinatorial model categories
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 15, 2022 at 9:12 | comment | added | Giulio Lo Monaco | That would be too strong for me, unfortunately. I can assume that $\mathbf{A}$ is precisely the subcategory of $\mathbf{M}$ inducing a given full subcategory $\mathcal{C} \subseteq N_{\Delta}(\mathbf{M}^{\circ})$, but this in turn should be a general subcategory | |
| Aug 12, 2022 at 18:29 | comment | added | Boris Chorny | What would you like to assume about 𝐀? Could it be reflective? | |
| Aug 11, 2022 at 8:21 | comment | added | Giulio Lo Monaco | I'm not so sure that that proof generalizes to $\infty$-categories, not in the straightforward way at least. However, I have an alternative proof that works up to my question above, so in the end you may use Vopenka if you want, but also I'd like to know if that holds in general. | |
| Aug 10, 2022 at 15:38 | comment | added | Tim Campion | Do you want to assume Vopenka? I believe that under VP, "the same proof" as Adamek and Rosicky, Thm 6.9 (performed in a presheaf $\infty$-category rather than the category of graphs), shows that every full subcategory inclusion into a presentable $\infty$-category preserves $\lambda$-filtered colimits for some $\lambda$. Then you can translate this into a model-categorical statement with enough co/fibrancy hypotheses. | |
| Aug 10, 2022 at 14:45 | history | asked | Giulio Lo Monaco | CC BY-SA 4.0 |