That is all copied from David Roberts’s answer here, see post #3 above. (Not sure why I didn’t explicitly cite the MO link, but I guess it was my first time editing the nLab.) Anyway, we should ask David about the source for this.
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]]>Guest #221: if that link is not working for you, please try clearing your cache or using another browser. Is the main nLab also not working for you?
]]>Guest #218 and #219:
Is this the wiki you’re referring to? I am able to access it and see edits as recently as today.
]]>I have reverted ncatlab.org to its December 2021 state, with the old instiki-forked software. The nForum should now be working as well. It may take some time for DNS changes to get propagated everywhere (clearing cache can help).
More details:
The issue with the nForum was just an expired SSL certificate. However, renewing it actually required me to have the DNS pointed back to Saunders instead of the new AWS server, just for our SSL provider LetsEncrypt to be able to verify the renewal request. (When I say “required me to”, that’s just because of my lack of access to / familiarity with AWS.)
After renewing the certificate, I reverted the DNS back to AWS. Somehow, this ended up breaking the nLab itself, and also re-breaking the nForum.
In view of this, and also of Urs’s independent urging, I re-reverted the DNS to Saunders, and re-configured the web server to show the old Instiki-based software.
I don’t have time to do much more right now, but I hope that in the near future, the nLab community can come to a consensus on the future of the nLab software. I think Richard’s new software looks exciting from what I’ve soon and I hope he is willing to reconsider his resignation, as it would be a shame for the tremendous amount of hard work he has done to go to waste. Perhaps we could carry out the migration to the new software in parallel, while the current version continues to exist and be editable? Surely it will not be too much work to, once the new system is ready, take the new edits after Dec 2021 and migrate just those to the new software.
]]>I am resigning, and leaving the technical administration of the nLab fully in the very capable hands of Richard Williamson.
]]>I had deleted that post and banned the author. The author of this post is this MO user. Most likely he renamed his GitHub account and caused the links above to move as well.
]]>Here are a couple excerpts from e-mails I received from Professor Lawvere in March 2016:
]]>In fact, he gave three extensive courses for students and postdocs here in Buffalo in 1973 and in May 1973 he made the qualitative advance described in his Colloqium talk. [I suggest that you change the reference to Gaeta’s notes; they represent one of the three Courses, NOT the Colloquium talk. Note that the Grothendieck Circle made the same mis-citation!]
Peter Gabriel (who unfortunately died this past November 24) had explained some of the same ideas at Oberwolfach in 1965-66, providing a context in which Grothendieck’s proposal seemed natural. For example, he emphasized the traditional view that the points of an algebraic space form a covariant functor on the category of field extensions of the base. The colimit of that functor gives the abstract set of points (= the prime ideals in the case of Spec); however, that colimit is not exact nor even product preserving, so that the category of abstract sets is not a good base topos unless the base field is algebraically closed.
[…]
There still exists considerable misunderstanding of these matters, so that, for example, fragments of the 1973 idea are pasted on top of the older 1960 view, leading in practice to complication, rather than simplification.
Grothendieck’s advice in his Colloquium talk was that 1960 ingredients (like Zariski opens etc.) are easily extracted from the category of functors, when needed.
[…]
The three courses of Grothendieck were recorded on tapes by Jack Duskin, and recently we had them transferred to a more modern medium. The historian of mathematics David Rowe in Mainz facilitated this transformation, with Michael Wright’s and of course our help. There are no other notes from the time, except Gaeta’s for ’algebraic geometry’, called ’functorial’ (except that the functorial aspect is not emphasized, as it was to be in the Colloquium Talk); the other two courses were ’Toposes’ and ’Algebraic Groups’ of which the audio version seems to be the only remnant.
Awesome! A static frontend is something I’ve thought about for a long time, but never actually got around to implementing. Needless to say I definitely support the idea. One question: why not just use Nginx’s built-in static server, surely that must be even faster than additionally going through your Go server?
]]>Cloudflare’s “Always Online” feature only caches a few pages, see here. Customizing the error message is indeed possible but unfortunately it is a premium feature. Pointing the DNS somewhere else would still be an option though.
]]>I believe the problem mentioned in #42 is now fixed. For example:
]]>Just to be clear, as an outsider to equivariant homotopy theory, I thought the following terminology was close to standard these days:
Genuine G-spectra: Invert all representation spheres in G-spaces. Modeled by spectral Mackey functors, for example.
Naive G-spectra: Invert S^1 in G-spaces. Modeled by presheaves of spectra on the orbit category.
Spectra with G-action: Functors BG -> Spectra, or Borel-complete genuine G-spectra.
Does “sometimes referred to as” mean “once, by Jacob, during the Thursday seminar, as a joke”?
Yes.
I think ’spectrum with a G-action’ is fine, and maybe also ’Borel G-spectrum’.
Well, those are the two suggestions I gave as well. I realize the above discussion doesn’t make sense anymore, after I renamed the pages. The page spectrum with G-action used to refer to what is now at naive G-spectrum.
All terminology with the word “naive” should probably be removed from the equivariant literature… (Especially because the ’official’ usage of ’naive G-spectrum’ from LMS- equivalent to presheaves of spectra on the orbit category- seems to be mostly unused in practice and also isn’t what people think it means.)
“Presheaves of spectra on the orbit category” is the definition I would give of naive G-spectrum as well. I would agree “naive” is not the best terminology, but is there a more standard option?
]]>Ok, done.
]]>Let me also mention a further argument for reserving some terminology for “a spectrum with a G-action”. In the special case when G is cyclic of prime order, we have simple models of naive and genuine G-spectra in terms of spectra with G-action:
A naive G-spectrum is a spectrum with -action, together with another spectrum (called the genuine fixed point spectrum) and a map ( = homotopy fixed points).
A genuine G-spectra is a spectrum with -action, together with another spectrum and morphisms ( = homotopy orbits). (Alternatively, you can specify a geometric fixed point spectrum and a map to the Tate construction.)
This is proven in:
The obvious definition of spectrum with G-action is just that: a spectrum with a G-action. This is even more naive than the notion discussed at spectrum with the G-action (which are sometimes called naive G-spectra), so these are sometimes called “doubly naive” G-spectra; they’re what you get if you start with the naive version of G-spaces, i.e. just spaces with G-action, and then naively stabilize. These doubly naive G-spectra can also be identified with a certain full reflective subcategory of genuine G-spectra whose objects are sometimes called “Borel-complete” G-spectra: they have the property that homotopy fixed points coincide with genuine fixed points with respect to all subgroups of (at least if is finite).
Anyway, I’m not an expert here, but maybe we should use a different terminology for spectrum with G-action.
]]>Yeah, good catch.
What appears to have happened is that all the HTML character entities on nLab pages have been replaced by their actual unicode equivalent characters.
This is the inadvertent result of a script I ran to fix any encoding issues in all the pages. I made a backup we could restore to, but I’m not sure unicode characters instead of HTML entities is a bad thing. I’d rather fix the iTeX issue, which seems like it shouldn’t be much work.
]]>That would help, yeah.
]]>@34: It could be a completely separate issue. I would have to reproduce the bug in order to diagnose it, which I haven’t been able to do when I tried just now.
]]>@33: I’m not sure that was caused by the latest changes. For example, using unicode in math commands doesn’t work here either:
and there haven’t been any changes to the nForum configuration. I would assume it’s just an iTeX issue. To be honest, I don’t even know whether this works in LaTeX. Of course in this instance it can be fixed by changing ⇸ to \twoheadrightarrow.
]]>I’m not aware of any restriction on the length of anchor names, no.
]]>Well the default library that Maruku was using for string scanning had the bug related to equation numbering. When I switched to a different string scanning library, this issue was fixed but then we started getting other errors on a lot of pages. The reason turned out to be that the second library wasn’t equipped to handle multibyte character sets like UTF-8. Once I figured out what was going on, it turned out to be easy to fix.
]]>Ok, I did not mean to spend that long on this… but I think it might really be fixed now. At least, Sandbox, category, topos and ring are all working.
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