Timeline for Is there an analog of Kan's $Ex^\infty$ functor for quasicategories?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 22, 2022 at 18:23 | answer | added | Dmitri Pavlov | timeline score: 6 | |
| Feb 11, 2021 at 14:59 | comment | added | Tim Campion | Just to record the disproof of right properness (which works either in Joyal or in $sSet^+$ and which I'll bet I learned from Alexander Campbell): $\Delta[1] \xrightarrow{d_1} \Delta[2]$ is a fibration, and $\Lambda^1[2] \to \Delta[2]$ is a weak equivalence, but the pullback $\partial \Delta[1] \to \Delta[1]$ is not a weak equivalence. | |
| Feb 11, 2021 at 14:54 | comment | added | Tim Campion | @SaalHardali I just realized -- I've been walking around thinking that marked simplicial sets are a right proper model structure, but they're not -- as I apparently knew a year ago. So the answer to your first comment is no, the there can be no fibrant replacement functor on $sSet^+$ which preserves finite limits and fibrations. | |
| Dec 11, 2019 at 23:13 | comment | added | Saal Hardali | Also in what sense does computing $GX$ for finite $X$ solves the word problem for groups? Presumably you could calculate $GX$ but still find it very hard to compare to $GY$ for any other $Y$. Similarly to how difficult it is to compare arbitrary Kan complexes to each other. Most likely you meant something more subtle which I missed. | |
| Dec 11, 2019 at 23:07 | comment | added | Saal Hardali | It could still be possible that such a fibrant replacement functor exists for the (co-)cartesian model structure on marked simplicial set right? That is, one that preserves finite limits and fibrations. | |
| Mar 24, 2019 at 23:35 | comment | added | Tim Campion | Note that if there is a fibrant replacement functor which preserves finite limits and fibrations, then the model category is right proper. Since the Joyal model structure is not right proper, any functorial fibrant replacement which is a filtered colimit of right adjoints must fail to preserve fibrations. In particular, the Joyal model structure does not admit a fibrant replacement functor which is a filtered colimit of right Quillen functors. | |
| Mar 24, 2019 at 23:29 | history | edited | Tim Campion | CC BY-SA 4.0 |
The fact that I put "$\infty$" as a subscript in this question has bothered me for years.
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| Dec 15, 2016 at 13:02 | comment | added | Tim Campion | Oh -- now I see this is essentially a duplicate of this question. | |
| Nov 20, 2016 at 0:18 | history | asked | Tim Campion | CC BY-SA 3.0 |