Timeline for Does "simplicial" commute with "Bousfield localization"?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2014 at 19:15 | vote | accept | Theo Johnson-Freyd | ||
| Nov 3, 2014 at 19:15 | comment | added | Theo Johnson-Freyd | @KarolSzumiło: Great. Incidentally, I advocate the following notation: $X^Y$ means $X$-valued presheaves on $Y$, and not functors. I would write $^YX$ for the category of $X$-valued copresheaves on $Y$. The reason is that I think of right modules as contravariant functors. | |
| Nov 3, 2014 at 19:05 | comment | added | Karol Szumiło | It should be also pointed out that $\Delta$ being an elegant Reedy category means that in the category of simplicial diagrams over $\Delta^{\mathrm{op}}$ the Reedy and injective model structures coincide. However, $\Delta^{\mathrm{op}}$ is not elegant and the same is not true for diagrams over $\Delta$. | |
| Nov 3, 2014 at 18:53 | comment | added | Tyler Lawson | @TheoJohnson-Freyd Right, that's a particular nicety of simplicial sets (essentially, cofibrations are levelwise monomorphisms) that doesn't have an analogue in general. | |
| Nov 3, 2014 at 18:43 | comment | added | Theo Johnson-Freyd | Or, no, I've misunderstood. For $M = \mathrm{sSet}$, they agree, not in general. My apologies. | |
| Nov 3, 2014 at 18:41 | comment | added | Theo Johnson-Freyd | Great. I agree that what I linked to does not define cofibrations levelwise. But I think that for $\Delta$, the Reedy and injective model structures agree? I would have to think a lot about how to prove that directly, but my impression was that it was reasonably known. The reference I know is to arxiv.org/abs/1110.1066, although the claim about $\Delta$ seems to be older. | |
| Nov 3, 2014 at 16:59 | history | answered | Tyler Lawson | CC BY-SA 3.0 |