Not signed in (Sign In)

A discussion forum about contributions to the nLab wiki and related areas of mathematics, physics, and philosophy.

Want to take part in these discussions? Sign in if you have an account, or apply for one below

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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

If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

- Discussion Type
- discussion topicquark-gluon plasma
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 4th 2018

am adding references, such as this one:

- Francesco Biagazzi, A. l. Cotrone,
*Holography and the quark-gluon plasma*, AIP Conference Proceedings 1492, 307 (2012) (doi:10.1063/1.4763537, slides pdf)

- Francesco Biagazzi, A. l. Cotrone,

- Discussion Type
- discussion topiccup product
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Urs
- Last Active Dec 4th 2018

added a paragraph and a reference to cup product, archiving the blog comment here

- Discussion Type
- discussion topicorbifold cohomology
- Category Latest Changes
- Started by Urs
- Comments 53
- Last comment by David_Corfield
- Last Active Dec 4th 2018

added references by Pronk-Scull and by Schwede, and wrote an Idea-section that tries to highlight the expected relation to global equivariant homotopy theory. Right now it reads like so:

On general grounds, since orbifolds $\mathcal{G}$ are special cases of stacks, there is an evident definition of cohomology of orbifolds, given by forming (stable) homotopy groups of derived hom-spaces

$H^\bullet(\mathcal{G}, E) \;\coloneqq\; \pi_\bullet \mathbf{H}( \mathcal{G}, E )$into any desired coefficient ∞-stack (or sheaf of spectra) $E$.

More specifically, often one is interested in viewing orbifold cohomology as a variant of Bredon equivariant cohomology, based on the idea that the cohomology of a global homotopy quotient orbifold

$\mathcal{G} \;\simeq\; X \sslash G \phantom{AAAA} (1)$for a given $G$-action on some manifold $X$, should coincide with the $G$-equivariant cohomology of $X$. However, such an identification (1) is not unique: For $G \subset K$ any closed subgroup, we have

$X \sslash G \;\simeq\; \big( X \times_G K\big) \sslash K \,.$This means that if one is to regard orbifold cohomology as a variant of equivariant cohomology, then one needs to work “globally” in terms of

*global equivariant homotopy theory*, where one considers equivariance with respect to “all compact Lie groups at once”, in a suitable sense.Concretely, in global equivariant homotopy theory the plain orbit category $Orb_G$ of $G$-equivariant Bredon cohomology is replaced by the global orbit category $Orb_{glb}$ whose objects are the delooping stacks $\mathbf{B}G \coloneqq \ast\sslash G$, and then any orbifold $\mathcal{G}$ becomes an (∞,1)-presheaf $y \mathcal{G}$ over $Orb_{glb}$ by the evident “external Yoneda embedding”

$y \mathcal{G} \;\coloneqq\; \mathbf{H}( \mathbf{B}G, \mathcal{G} ) \,.$More generally, this makes sense for $\mathcal{G}$ any orbispace. In fact, as a construction of an (∞,1)-presheaf on $Orb_{glb}$ it makes sense for $\mathcal{G}$ any ∞-stack, but supposedly precisely if $\mathcal{G}$ is an orbispace among all ∞-stacks does the cohomology of $y \mathcal{G}$ in the sense of global equivariant homotopy theory coincide the cohomology of $\mathcal{G}$ in the intended sense of ∞-stacks, in particular reproducing the intended sense of orbifold cohomology.

At least for topological orbifolds this is indicated in (Schwede 17, Introduction, Schwede 18, p. ix-x, see also Pronk-Scull 07)

- Discussion Type
- discussion topicequivariant suspension spectrum
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Dec 4th 2018

- Discussion Type
- discussion topichadron
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Dec 3rd 2018

added graphics of the light hadron masses from Fodor-Hoelbling 12

- Discussion Type
- discussion topicglueball
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 3rd 2018

- Discussion Type
- discussion topicTadakatsu Sakai
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 3rd 2018

- Discussion Type
- discussion topicShigeki Sugimoto
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 3rd 2018

- Discussion Type
- discussion topicflavour (particle physics)
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 3rd 2018

- Discussion Type
- discussion topiccolor charge
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 3rd 2018

- Discussion Type
- discussion topictensor product of abelian groups
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Dec 3rd 2018

have split off

*tensor product of abelian groups*from*tensor product*and expanded slightly

- Discussion Type
- discussion topicaxiom of separation
- Category Latest Changes
- Started by Mike Shulman
- Comments 30
- Last comment by Richard Williamson
- Last Active Dec 3rd 2018

As far as I can tell, Ehrhard’s definition of comprehension requires not just that the fibers have terminal objects but that these are preserved by the reindexing functors. This is automatic if the fibration is a bifibration, as in Lawvere’s version; it’s fairly explicit in Ehrhard’s formulation, and somewhat implicit in Jacobs’ but I believe still present (his “terminal object functor” must, I think, be a

*fibered*terminal object).

- Discussion Type
- discussion topiccontinuation-passing style
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 3
- Last comment by Sam Staton
- Last Active Dec 2nd 2018

I added some references to continuation-passing style, as well as a big rambling Idea section.

- Discussion Type
- discussion topicAlan Martin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 2nd 2018

- Discussion Type
- discussion topicFrancis Halzen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 2nd 2018

- Discussion Type
- discussion topicquark
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Dec 2nd 2018

- Discussion Type
- discussion topicGeorge Zweig
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 2nd 2018

- Discussion Type
- discussion topicLöwenheim-Skolem theorem
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Dec 2nd 2018

- Discussion Type
- discussion topicidentity type
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by nLab edit announcer
- Last Active Dec 2nd 2018

added to identity type a mentioning of the alternative definition in terms of inductive types (paths).

- Discussion Type
- discussion topicthin category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Dec 1st 2018

- Discussion Type
- discussion topicHoTT methods for homotopy theorists
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Dec 1st 2018

- Discussion Type
- discussion topiccartesian closed category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by nLab edit announcer
- Last Active Dec 1st 2018

Added a subsection to cartesian closed category, the functional completeness theorem. (To be expanded upon, eventually.)

- Discussion Type
- discussion topicAlessandro Strumia
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Dec 1st 2018

brief category:people-entry for hyperlinking references at

*Higgs field*,*flavour anomaly*, and*asymptotic safety (or not)*.

- Discussion Type
- discussion topicHiggs field
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Dec 1st 2018

added a brief historical comment to

*Higgs field*and added the historical references

- Discussion Type
- discussion topicstandard model of particle physics
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Dec 1st 2018

**Edit to**: standard model of particle physics by Urs Schreiber at 2018-04-01 01:15:37 UTC.**Author comments**:added textbook reference

- Discussion Type
- discussion topicD-brane
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Dec 1st 2018

- Discussion Type
- discussion topic(eso and full, faithful) factorization system
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 30th 2018

Just noticed that when this page is shown in a Google search, the link from the Google page does not work. It seems that the “+” sign that used to be in the entry title gets interpreted as a whitespace.

Therefore I am now changing the page name, replacing “+” by “and”. This should fix the problem, once Google picks up the change.

- Discussion Type
- discussion topicStieltjes integral
- Category Latest Changes
- Started by FrancoisL
- Comments 3
- Last comment by Todd_Trimble
- Last Active Nov 29th 2018

This page is dedicated to the Stieltjes integral. It is basically a generalization of integrals with respect to a function of bounded variation.

This page will present the main propperties of the Stieltjes integral and show its links with measure theory and other types of integral, mainly the Riemann integral, the Lebesguye integral and the Stieltjes integral.

- Discussion Type
- discussion topiccoherent logic
- Category Latest Changes
- Started by Mike Shulman
- Comments 11
- Last comment by nLab edit announcer
- Last Active Nov 29th 2018

I merged coherent formula into coherent logic and added redirects; I didn’t see a good reason to keep them separate. Perhaps the page should actually be called coherent theory to match with geometric theory, or vice versa, any thoughts?

- Discussion Type
- discussion topiccorecursion
- Category Latest Changes
- Started by David_Corfield
- Comments 24
- Last comment by Mike Shulman
- Last Active Nov 29th 2018

I thought it better to use $pred(n)$ rather than $n -1$ in the addition, since it’s supposed to apply to $\infty$.