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- Discussion Type
- discussion topicV_cb puzzle
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 1st 2021

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)

- Paolo Gambino, Martin Jung, Stefan Schacht,

- Discussion Type
- discussion topicinitial algebra of an endofunctor
- Category Latest Changes
- Started by anqurvanillapy
- Comments 2
- Last comment by nLab edit announcer
- Last Active Apr 1st 2021

- Discussion Type
- discussion topicRobin Terrisse
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2021

- Discussion Type
- discussion topicG-structure
- Category Latest Changes
- Started by zskoda
- Comments 27
- Last comment by Urs
- Last Active Mar 31st 2021

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 ?

- Discussion Type
- discussion topicfunny tensor product
- Category Latest Changes
- Started by Mike Shulman
- Comments 12
- Last comment by John Baez
- Last Active Mar 31st 2021

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.

- Discussion Type
- discussion topicDenis Nardin
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 31st 2021

brief category:people-entry, for the purpose of hyperlinking references at

*Parametrized Higher Category Theory and Higher Algebra*

- Discussion Type
- discussion topicstable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 31st 2021

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.

- Discussion Type
- discussion topicMatthias König
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2021

brief

`category:people`

-entry for hyperlinking references at*flavour anomaly*and*leptoquark*

- Discussion Type
- discussion topicMatthias Neubert
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2021

brief

`category:people`

-entry for hyperlinking references at*flavour anomaly*and*leptoquark*

- Discussion Type
- discussion topicJavier Fuentes-Martin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2021

brief

`category:people`

-entry for hyperlinking references at*flavour anomaly*and*leptoquark*

- Discussion Type
- discussion topicRoman Jackiw
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2021

added pointer to today’s

- Robert D. Pisarski,
*Roman Jackiw and Chern-Simons theories*(arXiv:2103.15868)

- Robert D. Pisarski,

- Discussion Type
- discussion topicSteffen Stern
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2021

brief

`category:people`

-entry for hyperlinking references at*higher curvature correction*

- Discussion Type
- discussion topichigher curvature corrections to D=11 supergravity -- references
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 31st 2021

a bare list of references, previously coded both at

*D=11 supergravity*and at*higher curvature correction*, now extracted here to be`!include`

-ed back there, for ease of synchronizing

- Discussion Type
- discussion topicD-brane charge quantization in K-theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 31st 2021

am finally giving this its own entry, to be split off (not done yet) from

*D-brane charge*and to be in parallel with*K-theory classification of topological phases of matter*

- Discussion Type
- discussion topictwistor fibration
- Category Latest Changes
- Started by Urs
- Comments 29
- Last comment by Urs
- Last Active Mar 31st 2021

- Discussion Type
- discussion topictwisted equivariant differential K-theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2021

am giving this finally a stub entry (i.e. on the combination of all of 1. twisted 2. equivariant and 3. differential) since I need to link to it from the Idea-section at

*K-theory classification of D-brane charge*, which I am finally writing.In lack of other available literature, I am taking the liberty of linking to our article-in-preparation titled

*Twisted Equivariant Differential non-abelian generalized cohomology*. We’ll have details available soon.

- Discussion Type
- discussion topicelliptic curve
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Richard Williamson
- Last Active Mar 31st 2021

added a chunk of some standard basics to

*elliptic curve – Definition over a general ring*.Also touched/briefly created various related entries, such as

*Weierstrass equation*,*Weierstrass elliptic function*,*cubic curve*,*j-invariant*etc.

- Discussion Type
- discussion topiccomplex projective 3-space
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Mar 31st 2021

for completeness and to satisfy links from

*Calabi-Penrose fibration*

- Discussion Type
- discussion topicViktoriya Ozornova
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Tim_Porter
- Last Active Mar 31st 2021

- Discussion Type
- discussion topictorsion subgroup
- Category Latest Changes
- Started by Richard Williamson
- Comments 1
- Last comment by Richard Williamson
- Last Active Mar 31st 2021

Linking to the new page torsion points of an elliptic curve.

- Discussion Type
- discussion topicMartina Rovelli
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Mar 31st 2021

- Discussion Type
- discussion topictorsion points of an elliptic curve
- Category Latest Changes
- Started by Richard Williamson
- Comments 1
- Last comment by Richard Williamson
- Last Active Mar 30th 2021

- Discussion Type
- discussion topicend
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Dmitri Pavlov
- Last Active Mar 30th 2021

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.)

- Discussion Type
- discussion topicLandau-Ginzburg model
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active Mar 30th 2021

finally cross-linked

*Landau-Ginzburg model*with*TCFT*and added a corresponding reference,prompted by this Physics.SE question

- Discussion Type
- discussion topicVitaly Ginzburg
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 30th 2021

brief

`category:people`

-entry for hyperlinking references at*superconductivity*and at*Landau-Ginzburg model*

- Discussion Type
- discussion topicBertrand Souères
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 30th 2021

brief

`category:people`

-entry for hyperlinking references at*higher curvature corrections*and*D=11 supergravity*

- Discussion Type
- discussion topicthe little n-disk operad is formal
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active Mar 30th 2021

- Discussion Type
- discussion topicinternal type theory
- Category Latest Changes
- Started by spitters
- Comments 2
- Last comment by Korman
- Last Active Mar 30th 2021

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

- Discussion Type
- discussion topiccolimit
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active Mar 30th 2021

- Discussion Type
- discussion topicKan extension
- Category Latest Changes
- Started by Mike Shulman
- Comments 57
- Last comment by Dmitri Pavlov
- Last Active Mar 30th 2021

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

- Discussion Type
- discussion topicRiccardo Barbieri
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 30th 2021

brief

`category:people`

-entry for hyperlinking references at*flavour physics*

- Discussion Type
- discussion topicRankin-Cohen bracket
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Mar 30th 2021

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.

- Discussion Type
- discussion topicflavour (particle physics)
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Mar 30th 2021

- Discussion Type
- discussion topicThomas Winyard
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 30th 2021

- Discussion Type
- discussion topicskyrmion
- Category Latest Changes
- Started by Urs
- Comments 38
- Last comment by Urs
- Last Active Mar 30th 2021

- Discussion Type
- discussion topiclimit
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Richard Williamson
- Last Active Mar 30th 2021

I toiuched the formatting and the hyperlinking of the paragraphs on compatibility of limits with other universal constructions.

Merged the previous tiny subsections on this to a single one, now

*Compatibility with universal constructions*.added the hyperlink to the stand-alone entry

*adjoints preserve (co-)limits*.Will create an analogous stand-alone entry for

*limits commute with limits*.

- Discussion Type
- discussion topicDaniel Kan
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 5
- Last comment by Urs
- Last Active Mar 30th 2021

- Discussion Type
- discussion topicfield of moduli
- Category Latest Changes
- Started by Richard Williamson
- Comments 1
- Last comment by Richard Williamson
- Last Active Mar 29th 2021

- Discussion Type
- discussion topicAn Exercise in Kantization
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 12
- Last comment by DavidRoberts
- Last Active Mar 29th 2021

- Discussion Type
- discussion topicrealizability topos
- Category Latest Changes
- Started by Todd_Trimble
- Comments 40
- Last comment by Mike Shulman
- Last Active Mar 29th 2021

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.

- Discussion Type
- discussion topicprojection formula
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 29th 2021

The MO question

*Where do all the projection formulas come from?*made me split off a dedicated entry*projection formula*. Also redirecting*reciprocity*.

- Discussion Type
- discussion topicI8
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 29th 2021

- Discussion Type
- discussion topicD=11 N=1 supergravity
- Category Latest Changes
- Started by David_Corfield
- Comments 7
- Last comment by Urs
- Last Active Mar 29th 2021

- Discussion Type
- discussion topicmass gap
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active Mar 29th 2021

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)

- Discussion Type
- discussion topicprobability theory
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Urs
- Last Active Mar 29th 2021

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

I added a reference there to

- Chris Heunen, Ohad Kammar, Sam Staton, Hongseok Yang,
*A Convenient Category for Higher-Order Probability Theory*, (arXiv:1701.02547)

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.]

- Chris Heunen, Ohad Kammar, Sam Staton, Hongseok Yang,

- Discussion Type
- discussion topicSourav Chatterjee
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 29th 2021

brief

`category:people`

-entry for hyperlinking references at*confinement*and*mass gap problem*and*lattice gauge theory*

- Discussion Type
- discussion topicopen problem of confinement -- references
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Mar 29th 2021

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)

- Discussion Type
- discussion topicFranz Wegner
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 29th 2021

brief

`category:people`

-entry for hyperlinking references at*lattice QFT*and at*Ising model*

- Discussion Type
- discussion topiclattice gauge theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 11
- Last comment by Urs
- Last Active Mar 29th 2021

- Discussion Type
- discussion topicAdS-QCD correspondence
- Category Latest Changes
- Started by Urs
- Comments 60
- Last comment by Urs
- Last Active Mar 29th 2021

- Discussion Type
- discussion topicLiping Zou
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by valeriadepaiva
- Last Active Mar 28th 2021

brief

`category:people`

-entry for hyperlinking references st*hadron supersymmetry*

- Discussion Type
- discussion topiccenter
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Mar 28th 2021

- Discussion Type
- discussion topicoctonionic projective space
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by zskoda
- Last Active Mar 28th 2021

starting something, for the moment just so as to record that

there is a homeomorphism

$\mathbb{O}P^2 \,\simeq\, S^{15} \underset{h_{\mathbb{O}}}{\cup} \mathbb{H}P_1$between the octonionic projective plane and the attaching space obtained from the octonionic projective line along the octonionic Hopf fibration.

- Discussion Type
- discussion topicclassifying space
- Category Latest Changes
- Started by Urs
- Comments 34
- Last comment by Urs
- Last Active Mar 28th 2021

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

- Discussion Type
- discussion topicStephen Mitchell
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 28th 2021

brief

`category:people`

entry, 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)

- Stephen Mitchell,

- Discussion Type
- discussion topicHagen Triendl
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 28th 2021

brief

`category:people`

-entry for hyperlinking references at*G-structures*and*supergravity*

- Discussion Type
- discussion topicmicrolocal sheaf theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Mar 28th 2021

- Discussion Type
- discussion topicsphere
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Mar 28th 2021

- Discussion Type
- discussion topiccategory of Lie algebras
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Mar 28th 2021

- Discussion Type
- discussion topicfiltered Lie algebra
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Mar 28th 2021