Hi,

Sorry if this has been discussed before. I want to cite the nLab in a paper. Is there a standard way to do this?

I am aware of efforts to have a ’journal of the nLab’, which I think is a great idea, although I haven’t been following the progress of this. Is there any suggestion that this could be adapted for ordinary nLab pages, as if to rubber-stamp them ’this page has been reviewed by experts in the community and been considered high-quality’?

Cheers, Jamie.

]]>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*

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.

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

Added the definition of “basic triples” of octonions, and the statement that they form a torsor over $Aut(\mathbb{O}) = G_2$.

]]>I see super-Cartan geometry is taking shape. Will Clifford algebras make an appearance in the The super-Klein geometry: super-Minkowski spacetime section?

Is there a higher super-Cartan way of thinking about what is at 3-category of fermionic conformal nets, about the String 2-group and superstrings, as here about the spin group and fermions.

]]>We are in the process of finalizing this article here:

Domenico Fiorenza, Hisham Sati, Urs Schreiber

*Super Lie $n$-algebra extensions, higher WZW models and super p-branes with tensor multiplet fields*

**Abstract.** We formalize higher dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the “FDA”-language used in the supergravity literature).
We show generally how the intersection laws
for such higher WZW-type sigma-model branes (open brane ending on background brane) are encoded precisely in (super-)$L_\infty$-extension theory and how the resulting “extended (super-)spacetimes” formalize spacetimes containing $\sigma$-model brane condensates. As an application we prove in Lie $n$-algebra homotopy theory that the complete super $p$-brane spectrum of superstring/M-theory is realized this way,
including the pure sigma-model branes (the “old brane scan”) but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional spacetime with an M2-brane condensate turns out to be the “M-theory super Lie algebra”. We also observe that in this
formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11-dimensional sugra/M-theory spacetime, and of (prequantum) S-duality for type II string theory. Finally we give the non-perturbative description of all this by higher WZW-type $\sigma$-models on higher super-orbispaces with higher WZW terms in higher differential geometry.

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

]]>I fixed the first sentence at *doctrine*. It used to say

A

doctrine, as the word was originally used by Jon Beck, is a categorification of a “theory”.

I have changed it to

The concept of

doctrine, as the word was originally used by Jon Beck, is a categorification of the concept of “theory”.

If you see what I mean.

Then I added to the References-section this:

]]>The word “doctrine” itself is entirely due to Jon Beck and signifies something which is like a theory, except appropriate to be interpreted in the category of categories, rather than, for example, in the category of sets; of course, an important example of a doctrine is a 2-monad, and among 2-monads there are key examples whose category of “algebras” is actually a category of theories in the set-interpretable sense. Among such “theories of theories”, there is a special kind whose study I proposed in that paper. This kind has come to be known as “Kock-Zoeberlein” doctrine in honor of those who first worked out some of the basic properties and ramifications, but the recognition of its probable importance had emerged from those discussions with Jon.

now I have finally the time to come back to this, as announced, and so I am now starting an entry:

*relation between type theory and category theory* .

So far there is just some literature collected. I now plan to extract the essence of Seely’s artice into the entry in some technical detail.

]]>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.

]]>stub for Hořava-Witten theory

]]>I came to think that the term *geometric type theory* for the type theory internal toi sheaf toposes should exists. Thanks to Bas Spitter for pointing out that Steve Vickers had already had the same idea (now linked to at the above entry).

Also created *geometric homotopy type theory* in this vein, with some evident comments.

Just collecting together things on the list to implement/look into, to make it a little easier and anybody else interested in contributing to keep an overview.

1) Import of HoTT special year pages into the nLab. Request of Mike over email.

2) Speed up of page loading on the nLab. Last touched on by Urs here. See also the experiments with a static frontend, discussed here.

3) Update nForum announcements made within 30 minutes rather than post new announcements, to mirror the behaviour of the nLab. Last touched on here.

4) Make tool for handling references in the nLab. Last discussed here.

5) Save and display nLab page title changes in the revision history. See here.

6) Fix bugs in the nLab’s display of the diff in mathematics the revision history. (See more or less any diff where mathematics is involved).

7) Automatically convert links posted verbatim in the nForum to actual links rather than plain text.

I think that’s everything that has been raised so far. Things may soon be added to the list, e.g. the thoughts Urs had in #68 and #70 here.

Let me know if there’s anything else I should add.

]]>Defined a crossed G-set in an explicit way, and described explicitly the braiding on the category of crossed G-sets. Gave reference to *Braided tensor categories* by Joyal and Street. Plenty more could be added (e.g. more categorical point of view on what a crossed G-set is, Drinfeld centres, …).

I changed it to the usual definition.

If the nonstandard definition is equivalent to the usual one, I'd love to know why! But I don't see how you get two hexagons from one, even given compatibility with the unit object.

(Of course for a

I also beefed up the definition at symmetric monoidal category so the poor reader doesn't need to run back to braided monoidal, then monoidal. ]]>

Quick idea section for call-by-push-value

]]>Started linear-non-linear logic, more to come.

]]>Does anyone have access to

AARNE RANTA, Constructing possible worlds, Volume 57, Issue 1-2, pages 77–99, April 1991 ?

DOI: 10.1111/j.1755-2567.1991.tb00541.x

I think he treats possible worlds there in terms of contexts.

]]>My last two attempts to uoload files to the nLab server failed: after hitting “upload” the page would wait forever for a reply.

This happened to me in the entry Alexandrov space, where you can still see the unsatisfied link to the pdf in the list of references.

Now it is happening to me with another file on my personal web.

I think the problem arises also when file sizes are larger than the maximal size determined in the web-preferences.

But this cannot be the case here. Both files in question are small compared to what I usually upload.

Any ideas?

]]>split off “neutral element” from “monoid” (to which it used to be redirecting)

Just such as to clesan up the link structure a little.

]]>I could not understand the proof of the fact that if a vector space $V$ over a field $k$ is dualisable in the monoidal category $\mathbf{Vect}_k$ then it should be finite dimensional. I understand that the image of $k$ under the unit is a $1$-dimensional subspace, but why should this imply the finite dimensionality of $V$? I would be thankful if someone could provide me the complete proof or a pointer to it.

With my regards,

partha

]]>New entry PBW theorem and stub primitive element. Related new stubs filtered ring and associated graded ring with redirects filtered algebra, associated graded algebra.

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