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• I did not change anything, I would not like to do it without Urs’s consent and some opinion. The entry AQFT equates algebraic QFT and axiomatic QFT. In the traditional circle, algebraic quantum field theory meant being based on local nets – local approach of Haag and Araki. This is what the entry now describes. The Weightman axioms are somewhat different, they are based on fields belonging some spaces of distributions, and 30 years ago it was called field axiomatics, unlike the algebraic axiomatics. But these differences are not that important for the main entry on AQFT. What is a bigger drawback is that the third approach to axiomatic QFT if very different and was very strong few decades ago and still has some followers. That is the S-matrix axiomatics which does not believe in physical existence of observables at finite distance, but only in the asymptotic values given by the S-matrix. The first such axiomatics was due Bogoliubov, I think. (Of course he later worked on other approaches, especially on Wightman’s. Both the Wightman’s and Bogoliubov’s formalisms are earlier than the algebraic QFT.)

I would like to say that axiomatic QFT has 3 groups of approaches, and especially to distinguish S-matrix axiomatics from the “algebraic QFT”. Is this disputable ?

For a treatment in homotopy type theory see

• Dan Frumin, Herman Geuvers, Léon Gondelman, Niels van der Weide, Finite Sets in Homotopy Type Theory, (pdf)
• created computational trinitarianism, combining a pointer to an exposition by Bob Harper (thanks to David Corfield) with my table logic/category-theory/type-theory.

• In discrete fibration I added a new section on the Street’s definition of a discrete fibration from $A$ to $B$, that is the version for spans of internal categories. I do not really understand this added definition, so if somebody has comments or further clarifications…

Sounds interesting

We would like to mention that a structure similar to categorical symmetry was found previously in AdS/CFT correspondence, [63–65] where a global symmetry $G$ at the high-energy boundary is related to a gauge theory of group $G$ in the low-energy bulk. In this paper, we stress that the categorical symmetry encoded by the bulk $G$-gauge theory not only contains the $G$ symmetry at the boundary, it also contains a dual algebraic higher symmetry $\tilde{G}^{(n-1)}$ at the boundary.

• I created the article multisimplicial set.

It seems that I triggered some bug in Instiki that prevents it from rendering displayed formulas correctly.

The article compiles just fine in TeX, so this is clearly a bug.

In fact, Instiki seems to insert some new text:

All this “chunk” and “wikichunklink” stuff is clearly a bug.

• a stub entry, for the moment just in order to make some links work

• Create a stub.

• added the Hurewicz model structure as an example of 2-trivial model structure

Daniel Teixeira

• Create a stub for this concept.

• Changed typo’d “pyschoaccoustics” to correct “psychoacoustics”.

Anonymous

• Strangely, we don’t seem to have an nForum discussion for probability theory.

I added a reference there to

It replaces the category of measurable spaces, which isn’t cartesian closed, with the category of quasi-Borel spaces, which is. As they point out in section IX, what they’re doing is working with concrete sheaves on an established category of spaces, rather like the move to diffeological spaces.

[Given the interest in topology around these parts at the moment, we hear of ’C-spaces’ as generalized topological spaces arising from a similar sheaf construction in C. Xu and M. Escardo, “A constructive model of uniform continuity,” in Proc. TLCA, 2013.]

• For no particular reason, I have added another illustrating graphics to the entry, taken from Fig 1.3 in Apostol 1973.

• I noticed that the entry analysis is in a sad state. I now gave it an Idea-section (here), which certainly still leaves room for expansion; and I tried to clean up the very little that is listed at References – General

• brief category:people-entry for hyperlinking references

• sSet is not naturally a reflective subcategory of sSet_sym. I guess the original author meant simplicial complexes

Christian

• Started an article on monoidal monad. An earlier redirect had sent it over to Hopf monad which is something that Zoran was working on, but I think it deserves an article to itself, with discussion of the relation to commutative monads, etc. (which I have started).

• starting something. Not done yet but need to save

• The term “tensor network”, while essentially just a synonym for “string diagram”, has in recent years become widely used and now fully established in quantum physics, especially in its use for discussion of holographic entanglement entropy. It needs a page of its own, if only to point to string diagram while also listing the relevant physics references

• R. Catenacci, P.A. Grassi, S. Noja, Superstring Field Theory, Superforms and Supergeometry (arXiv:1807.09563)
• Since it was mentioned by Urs on g+, I thought I’d start mysterious duality. Maybe not a great name when someone discovers how it works (as someone claims to have done here).

• re-did the typesetting of the adjoint triple with TikZ

• Fixed pdf link to “Towards an understanding of Girard’s transcendental syntax”

ALH

• I have changed the title of this article, as well as references to the object within it. Use of the term “Hawaiian Earring” is objected to by Hawaiian mathematicians. Please see these two threads, one by native Hawaiian and math PhD Dr. Marissa Loving, and the other by an expert on the Hawaiian Earring, Dr. Jeremy Brazas.

I have retitled the article “Shrinking wedge of circles”, which is the name used for this space in Hatcher’s “Algebraic Topology”. I have a retained a note in the body of the article that the space is sometimes referred to as the “Hawaiian earring space”.

This small change in name helps to make mathematics a more inclusive and just field, especially in consideration of the historical marginalization and exclusion of indigenous mathematicians. By taking this action, the nLab site can help to spread a change in language more widely, including on other math reference sites.

I hope that this change is readily accepted and approved by the nLab community. Thank you!

Justin Lanier

• Done, but now there is some overlap.

• Reorganization and expansion to consider constructive variants.

• Added a diagram at commutative algebraic theory using the totally awesome SVG Editor.

it now does itex!

This was a ridiculously simple diagram to do.

• Valentine Bargman, Note on Wigner’s theorem on symmetry transformations, Journal of Mathematical Physics 5.7 (1964): 862-868 (doi:10.1063/1.1704188)
• In the article connection on a cubical set the definition of a connection uses two types of maps, denoted Γ^+_i and Γ^-_i. Roughly, the former corresponds to a map of cubes that takes the minimum of some coordinates, whereas the latter takes the maximum of some coordinates.

However, in the book by Brown-Higgins-Sivera in Definition 13.1.3, page 446, only the maps Γ^-_i are used. There they are denoted simply by Γ_i. The paper by Maltsiniotis about the strict test category of cubes with connection also uses the same definition.

Which definition is correct? What is the reference for nLab’s definition and why does it deviate from the definition of Brown-Higgins-Sivera?

• In the past we had some discussion here about why simplicial methods find so much more attention than cubical methods in higher category theory. The reply (as far as I am concerned at least) has been: because the homotopy theory = weak oo-groupoid theory happens to be well developed for simplicial sets and not so well developed for cubical sets. Historically this apparently goes back to the disappointment that the standard cubical geometric realization to Top does not behave as nicely as the one on simplicial sets does.

Still, it should be useful to have as much cubical homotopy theory around as possible. Many structures are more naturally cubical than simplicial.

So as soon as the Lab comes up again (we are working on it...) I want to create a page model structure on cubical sets and record for instance this reference here:

• Add $\#$-connected for general inequalities.

I was chatting with Robin Cockett yesterday at SYCO1. In a talk Robin claims to be after

The algebraic/categorical foundations for differential calculus and differential geometry.

It would be good to see how this approach compares with differential cohesive HoTT.

• tried to improve the entry coproduct a little

• I have touched the formatting at direct sum and then expanded a little:

1. Added a paragraph to the Idea-section such that something familiar is mentioned right at the beginning;

2. Expanded on the example of direct sums in $Ab$ by drawing the cocone diagrams and explicitly mentioning the universal property.

3. Mentioned the relation to formal linear combinations.

4. Mentioned the examples of direct sums of modules.

• New.

• added below the very first definition at kernel a remark that spells out the universal property more explicitly. Also added mentioning of some basic examples.

• Eventually I’d like to connect quantum contextuality, contextuality in categorical logics, and the axiomatic approaches to QFT.