Thanks for the feedback, Tim!

I’ve now tidied up a few things, including providing the correct month and year when citing a specific revision (as mentioned in #28), and pushed the commit to github.

The unicode-to-ascii/latex hardcoding that I mentioned in #28 is in this file, in the method on lines 112-186 for ascii, and lines 215-296 for LaTeX. Hopefully it is fairly clear what is going on even if you do not know Python or how to program: a line

"ß": "ss"

for example means replace ß by ss. Just ask if you would like me to explain something.

Please do check these conversions: for example, as mentioned in #28, I have not checked the LaTeX that results for most of them. I have attempted to make the conversions as uncontroversial as possible: if there is any possible reason for discontent that I am aware of, I have gone with the simple ’remove the diacritic’ or ’find the closest looking symbol in ASCII’ approach. For Norwegian letters å, æ, ø I have converted to aa, ae, oe, and similarly for German ä, ö, ü (handling some exceptions for Finnish in the first case), because these are standard. If you disagree with anything or wish to correct it, just let me know here and I’ll make the change; or, even better, make a pull request at github!

]]>added the famous quote here

]]>made explicit the alternative form of the definition (here) in terms of adjoining a generator and imposing relations

]]>cross-linked with *super Klein geometry*

made explicit how super-Minkowski is a super-group quotient, and similarly for *super anti de Sitter spacetime*

cross-linked with *super Klein geometry*

References like this are about *super anti de Sitter spacetime* (we should cross-link!). There are very many of such references, since this is what enters the AdS-CFT correspondence.

Added a statement (here) concerning projecting out $\mathbb{H}$ from $\mathbb{O}$.

]]>Almost all work here seems to be by physicists for particular applications rather than a pure mathematical account, so perhaps only worth adding if the physics is interesting. E.g., how about

- Jaume Gomis, Dmitri Sorokin, Linus Wulff,
*The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes*, (arXiv:0811.1566)

which deals with superspaces like the type IIA superspace $OSp(8|4)/SO(7) \times SO(1,3)$?

]]>Thanks!

]]>added missing cross-link to *super Klein geometry*

I came across mention of homogeneous spaces for supergroups, and since we don’t have an entry for this I’ve started one.

The quotients for those two superspheres are cited in the literature, but I haven’t checked them.

]]>added statement and proof (here) that the product of all the seven imaginary quaternions with each other is $\pm 1$.

]]>how would one know one had found the elusive M-theory?

The established method is to see if the computations, drawn on a blackboard, invoke thunder and lightning.

Seriously, to complete this program, one will delve more deeply into dynamics. Presently what we have is a fair bit of indications that lifting 11d SuGra to M-theory means to lift its description as the ordinary torsion-free super Cartan geometry modeled on $\mathbb{R}^{10,1\vert \mathbf{32}}$ to some kind of torsion-free equivariant higher super-Cartan geometry, because we show that super tangent space wise this produces pretty much all the expected “topological” objects and dualities.

In a naive picture this gives a higher kind of differential equations, generalizing those of torsion-freedom for $\mathbb{R}^{10,1\vert \mathbf{32}}$-Cartan geometry, and one might consider perturbative quantization of these differential equations and try to compare the resulting scattering matrices to those of the various superstring theories.

But I suspect that as we keep understanding the mathematical structure appearing here better, we will find that it wants to do something a little different than what this naive picture suggests. We have to see.

]]>That looks good to me. I especially like that the Home Page has a ’cite’ button as a general citation to the nLab should direct to that page. Great.

]]>A Bibtex link at the bottom of nLab pages is a great idea! Most journal web sites which have an “export citation” feature seem to do it by a downloadable text file; personally I would prefer just a web page with some plaintext that I can copy and paste, but either way is fine.

Now implemented. In the menu at the bottom of every page or revision page, there is now a ’Cite’ option, which leads to a page at a new /cite endpoint with a .bib entry for ascii and unicode. See the menu at the bottom of étale cohomology for example, or étale cohomology (revision 31). Direct links to the ’cite’ page in these two cases are

https://ncatlab.org/nlab/show/%C3%A9tale%20cohomology/cite

and

https://ncatlab.org/nlab/revision/%C3%A9tale%20cohomology/31/cite.

Just let me know suggestions for improvement.

The month and year for the citation to a specific revision (rather than the current page) need to be set to the date of the revision, not the current date; I’ll fix that tomorrow. I’ll also post to github then; a bit too tired for that now. To handle unicode to ascii/latex conversion, since there is no generic way to do it, I’ve basically just hard-coded the conversion for every non-ascii symbol currently occurring in a page title (my favourite is 道德经, for which I’ve simply used the romanisation); it will be great if someone can look over that when I post to github, because I’ve not tested my hard-coding for all the possibilities.

]]>Added a link to the retyped version of SGA 4 1/2.

]]>A naive question no doubt, but how would one know one had found the elusive M-theory? Do the checks go beyond that it has the 5 string theories and 11-d supergravity as some kinds of limiting case?

For instance, the gauge enhancements shown in slides 43-45 come out “as predicted by the folklore on M-theoretic gauge enhancement”, and this folklore derives from gauge enhancement in (some of) the string theories?

]]>We should have an nLab conference one day.

This is the sort of the thing I imagine might be able to be funded if we were to obtain a grant, as discussed for instance in #14-#19 here.

Were you able to speak with Steve Awodey at the meeting, Mike? If not, how shall we proceed? I would have thought we should begin preparing something and applying sooner rather than later.

]]>Yes, but that 2-theory is not what these authors refer to by “type theory”. They speak of the 2-category *“of type theories”* and their theorem shows that “a type theory”, in their sense, is the same, up to equivalence, as a category that is a model for a type 1-theory. What these authors call “type theories” are what Mike suggests to call “type 0-theories”.

Isn’t that Theorem 3.2 further up the levels? Surely the theorem itself concerns a doctrine (2-theory) and the individual ML dependent type theories are 1-theories.

]]>Yes, “heard your voice”. I think maybe you were there at an impromptu talk that James Dolan gave to a handful of people.

We should have an nLab conference one day. I met Todd once in the last millennium. Aside from Urs, I don’t think I’ve met anyone else here.

]]>Brief idea of the *E-string*, pointer to and snippet from one reference that makes it nicely explicit.

I am compiling this and related entries because we have a clean mathematical formalization of this zoo of structures now in terms of equivariant super homotopy theory (as surveyed here). Once everything is cleaned up and published, I will try to go through all the entries and accompany the vague Idea-sections with some solid mathematics.

]]>Expanded the Idea-section slightly to include also the type I case, hence the picture of the triple of dualities

$\array{ HE &\overset{KK/\mathbb{Z}^A_2}{\leftrightarrow}& M &\overset{KK/\mathbb{Z}^B_2}{\leftrightarrow}& I' \\ \mathllap{T}\updownarrow && && \updownarrow \mathrlap{T} \\ HO && \underset{\phantom{A}S\phantom{A}}{\leftrightarrow} && I }$ ]]>