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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• am starting something. So far this is just a glorified pointer to today’s informative:

• Paolo Gambino, Martin Jung, Stefan Schacht, The $V_{c b}$ puzzle: an update (arXiv:1905.08209)
• Updated the linkref weak initial algebras' toweak inital’ (a.k.a. ‘weakly initial’)

• Page created, but author did not leave any comments.

• I do not understand the entry G-structure. G-structure is, as usual, defined there as the principal $G$-subbundle of the frame bundle which is a $GL(n)$-principal bundle. I guess this makes sense for equivariant injections along any Lie group homomorphism $G\to GL(n)$. The entry says something about spin structure, warning that the group $Spin(n)$ is not a subgroup of $GL(n)$. So what is meant ? The total space of a subbundle is a subspace at least. Does this mean that I consider the frame bundle first as a (non-principal) $Spin(n)$-bundle by pulling back along a fixed noninjective map $Spin(n)\to GL(n)$ and then I restrict to a chosen subspace on which the induced action of Spin group is principal ?

• Finally created funny tensor product. This is not really a very good name for a serious mathematical concept, but I don’t know of a better one.

• I have tried to improve the list of references at stable homotopy theory and related entries a bit. I think the key for having a satisfactory experience with the non-$\infty$-categorical literature reflecting the state of the art, is to first have a general but quick survey, and then turn for the details of highly structured ring spectra to a comprehensive reference on S-modules or orthogonal spectra. So I have tried to make that better visible in the list of reference.

I find that for the first point (general but quick survey) Malkiewich 14 is the best that I have seen.

Of the highly structured models, probably orthogonal spectra maximize efficiency. A slight issue as far as references go is that the maybe best comprehensive account of their theory is Schwede’s Global homotopy theory, which presents something more general than beginners may want to see (on the other hand, beginners often don’t know what they really want). In any case, I have kept adding this book reference as a reference for orthogonal spectra, joint with the comment that the inclined reader is to chooce the collection $\mathcal{F}$ of groups as trivial, throughout.

• added pointer to today’s

• starting something

• Stub for Viktoriya Ozonova.

• Created to ’ungrey’ a link.

• Gave the definition, and collected some key Galois-theoretic observations. As usual, would be nice with some explicit examples if someone has the energy!

• added the statement of the Fubini theorem for ends to a new section Properties.

(I wish this page would eventually give a good introduction to ends. I remember the long time when I banged my head against Kelly’s book and just didn’t get it. Then suddenly it all became obvious. It’s some weird effect with this enriched category theory that some of it is obvious once you understand it, but looks deeply mystifying to the newcomer. Kelly’s book for instance is a magnificently elegant resource for everyone who already understands the material, but hardly serves as an exposition of the ideas involved. I am hoping that eventually the nLab entries on enriched category theory can fill this gap. Currently they do not really. But I don’t have time for it either.)

• the idea and some references

• Created a stub for internal type theory to collect some references. At some point we could move more from Mike’s blog post.

• Redirect: colimit functor.

• I think the line between the two types of Kan extension (weak versus pointwise) is drawn at the wrong place. Am I missing something?

• brief category:people-entry for hyperlinking references at flavour physics

• A bare minimum on Rankin-Cohen brackets and deformation. I will do later an entry on related Jordanian twists, kind of Drinfeld twists (invertible counital 2-cocycles on bialgebras) which I worked on recently with collaborators in Zagreb. However, my new interest comes from a project in Hradec on geometry of foliations. Note that there are two Cohen’s in the subject – different initials are not typoi.

• stub entry, for the moment just so as to satisfy links

• brief category:people-entry for hyperlinking references at Skyrmion

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

• Added a redirect “Kan”.

• A brief idea section and one form of the definition. An example would be nice, if somebody has energy to add one! No doubt much more could usefully be said.

• Added a link to the nCafé discussion.

• I decided it would be a good idea to split off realizability topos into a separate entry (it had been tucked away under partial combinatory algebra). I’ve only just begun, mainly to get down the connection with COSHEP. A good (free, online) reference is Menni’s thesis.

• an entry to glorify the combination

$I_8 \;\coloneqq\; \tfrac{1}{48} \Big( p_2 \;-\; \big( \tfrac{1}{2} p_1\big)^2 \Big)$

seriously, I’ll need to refer to this from various other entries, so it’s useful to have a link

• Some $\times$ were written as $x$, so fixed. There were sign changes going on that I didn’t understand, $p_2 - (\frac{1}{2}p_2)^2$ and $p_2 + (\frac{1}{2}p_1)^2$.

• I am trying to collect citable/authorative references that amplify the analog of the mass gap problem in particle phenomenology, where it tramslates into the open problem of computing hadron masses and spins from first principles (due to the open problem of showing existence of hadrons in the first place!).

This is all well and widely known, but there is no culture as in mathematics of succinctly highlighting open problems such that one could refer to them easily.

I have now created a section References – Phenomenology to eventually collect references that come at least close to making this nicely explicit. (Also checked with the PF community here)

• 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.]

• a bare sub-section with a list of references – to be !included into relevant entries – mainly at confinement and at mass gap problem (where this list already used to live)

• I fixed a broken link to Guy Moore’s lectures

• starting something. Not done yet but need to save

• I changed a typo in the definition of the center of a Lie algebra, which was

“…all elements $z\in L$ such that $[l,z]=0$ for all $z\in L$”.

Now it is

“…all elements $z\in L$ such that $[l,z]=0$ for all $l\in L$”.

Vinícius Bernardes da Silva

• I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.

I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.

In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes

• brief category:peopleentry, for hyperlinking the lecture notes

• Stephen Mitchell, Notes on principal bundles and classifying spaces, Lecture Notes. University of Washington, 2011 (pdf)

that are referenced at classifying space, Borel construction and elsewhere

(hope I identified the author correctly)

• correct author name

Anonymous

• subdivided the Properties-section into subsections; added subsection for branched coverings of $n$-spheres

• Created.

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