Timeline for Which maps of simplicial sets geometrically realize to fibrations?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 17, 2019 at 23:04 | comment | added | Mike Shulman | @TimCampion beats me! It would also be interesting to characterize those $f$ such that ${\rm Ex}^\infty(f)$ is a Kan fibration. | |
| Jan 17, 2019 at 17:13 | comment | added | Tim Campion | Here's something that's bugging me: is it the case that $|f|$ is a Serre fibration iff $Ex^\infty(f)$ is a Kan fibration? | |
| Jan 14, 2019 at 17:40 | answer | added | John Rognes | timeline score: 4 | |
| Jan 12, 2019 at 21:28 | comment | added | Dan Ramras | If you want a simple explicit example of a map that is not a Kan fibration but whose realization is a Serre fibration, just take a simplicial set $X$ that is not a Kan complex, and map it to a point. | |
| Jan 12, 2019 at 3:39 | comment | added | Mike Shulman | @TimCampion Hmm, probably? | |
| Jan 12, 2019 at 3:06 | comment | added | Tim Campion | Probably I've been spouting nonsense. Anyway, now I'm trying to think of an explicit example of a map which is not a Kan fibration but whose realization is a Serre fibration. Is the quotient map out of $\Delta[2]$ which collapses the edge from $0$ to $1$ an example? | |
| Jan 12, 2019 at 0:41 | history | edited | Mike Shulman | CC BY-SA 4.0 |
Clarified the meaning of Hurewicz fibrations being closed under pushout of cofibrations
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| Jan 12, 2019 at 0:39 | comment | added | Mike Shulman | @TimCampion Ah, yes. Now I see how my statement was easy to misinterpret. I'll edit the question. | |
| Jan 11, 2019 at 18:14 | comment | added | Mike Shulman | @TimCampion Well, if there's a useful condition that includes assumptions on $X$ and $Y$, that would be something, although I'd prefer one that's only about the map. I don't see the relevance of either of your two links, can you explain? The closure of Hurewicz cofibrations under pushout along Hurewicz cofibrations is in the paper of Clapp linked to in the answer I linked to. And I don't understand your second comment; I didn't claim that every pushout of a Serre fibration along a cofibration is a Hurewicz fibration. | |
| Jan 11, 2019 at 17:22 | comment | added | Tim Campion | Are $X$ and $Y$ are Kan complexes (may simplify things)? quasicategories? general simplicial sets? If you don't want to assume that $X$ and $Y$ are Kan complexes, then there are various sufficient but not necessary conditions that people have considered -- cf Rezk's note or this question. This comes up e.g. in all kinds of delooping machine technology. Also do quasifbrations suffice? BTW why are Hurewicz fibrations closed under pushout along (Hurewicz?) cofibrations? | |
| Jan 10, 2019 at 17:03 | history | asked | Mike Shulman | CC BY-SA 4.0 |