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- Discussion Type
- discussion topicdiffeological space
- Category Latest Changes
- Started by Urs
- Comments 70
- Last comment by zskoda
- Last Active Mar 12th 2021

seeing Eric create diffeology I became annoyed by the poor state that the entry diffeological space was in. So I spent some minutes expanding and editing it. Still far from perfect, but a step in the right direction, I think.

(One day I should add details on how the various sites in use are equivalent to using CartSp)

- Discussion Type
- discussion topicFisher metric
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Mar 12th 2021

- Discussion Type
- discussion topicsemi-abelian category
- Category Latest Changes
- Started by DavidRoberts
- Comments 2
- Last comment by Urs
- Last Active Mar 12th 2021

Moving discussion here and summarizing content in the text

+– {: .query} Mike: Why only rings without units (that is, rngs)? Intuitively, what important properties do the above listed examples share that are not shared by rings with units?

Zoran Skoda: I want to know the answer as well. It might be something in the self-dual axioms. For unital rings artinian implies noetherian but not other way around; though the definitions of the two notions are dual.

*Toby*: The category of unital rings and unitary ring homomorphisms has no zero object.Mike: Ah, right. Is it protomodular? I think I will understand this definition better from some non-examples that violate each clause individually.

walt: It is protomodular. This follows from the main theorem of

*Characterization of Protomodular Varieties of Universal Algebra*by Bourn and Janelidze. By that theorem any variety that contains a group will be protomodular. Unital rings only fail to be semiabelian for the trivial reason that ideals aren’t subrings.=–

Maybe the result on protomodularity (with citation) mentioned by walt citing Bourn and Janelidze should be moved to CRing (and also Ring, if it holds for non-commutative rings).

- Discussion Type
- discussion topiccosmological constant
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Mar 12th 2021

I have added a comment and collected some references on the renormalization freedom in the cosmological constant: here

I have cross-linked this with related entries:

*renormalization*,*perturbative quantum gravity*and*stress-energy tensor*

- Discussion Type
- discussion topicMalcev category
- Category Latest Changes
- Started by Keith Harbaugh
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active Mar 12th 2021

- Discussion Type
- discussion topicpositronium
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 12th 2021

- Discussion Type
- discussion topicsuper 4-brane in 9d
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 11th 2021

brief page for one more entry in the

*brane scan*, on occasion of today’s- Meer Ashwinkumar, Lennart Schmidt, Meng-Chwan Tan, Section 2 of:
*Matrix Regularization of Classical Nambu Brackets and Super $p$-Branes*(arXiv:2103.06666)

- Meer Ashwinkumar, Lennart Schmidt, Meng-Chwan Tan, Section 2 of:

- Discussion Type
- discussion topicbrane scan
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 11th 2021

I gave the brane scan table a genuine $n$Lab incarnation and included it at

*Green-Schwarz action functional*and at*brane*.

- Discussion Type
- discussion topicquantization of M2-brane to matrix model -- references
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 11th 2021

- Discussion Type
- discussion topicde Sitter spacetime
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Mar 11th 2021

added pojnter to Maldacena-Nunez 01

- Discussion Type
- discussion topicPicard scheme
- Category Latest Changes
- Started by hilbertthm90
- Comments 7
- Last comment by nLab edit announcer
- Last Active Mar 11th 2021

Modulo the definition, I’ve created Picard scheme. One thing I couldn’t tell, is there a standard term in nlab for the “fiber category” of a stack? I mean if $F:C\to D$ fibers $C$ over $D$ then if you pick some object $X$ from $D$ the category $C_X$ consisting of objects that go to $X$ and morphisms that go to $id_X$.

- Discussion Type
- discussion topicMalcev variety
- Category Latest Changes
- Started by Todd_Trimble
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active Mar 11th 2021

I added some material to Mal’cev variety, namely proofs showing the various characterizations are equivalent, and a brief Examples section.

- Discussion Type
- discussion topicMalcev completion
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active Mar 11th 2021

- Discussion Type
- discussion topicAnatoly Malcev
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 3
- Last comment by Dmitri Pavlov
- Last Active Mar 11th 2021

- Discussion Type
- discussion topicquantum spin Hall effect
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by zskoda
- Last Active Mar 11th 2021

Just to highlight that in rev 2, from Oct. 2013 Xiao-Gang Wen added a remark claiming that the single reference given here is no good.

Wen added the analogous comment to

*topological insulator*in rev 5, from Oct 2013(I haven’t looked into it yet, just highlighting the edit for the moment, which seems to have gone unnoticed.)

- Discussion Type
- discussion topicEdward Bierstone
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 11th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant bundle*

- Discussion Type
- discussion topicuniversal principal bundle
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 11th 2021

I have finally created a stub entry for

*universal principal bundle*(which used to redirect to*universal principal infinity-bundle*).

- Discussion Type
- discussion topicMona Merling
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 11th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant principal bundle*

- Discussion Type
- discussion topicMitutaka Murayama
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 11th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant bundle*

- Discussion Type
- discussion topiccoherent state
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by Urs
- Last Active Mar 11th 2021

I changed back the name of the page to coherent state. Though it is usually considered in quantum mechanics, and the name is still correct, as a specialist in the area of coherent states, I have almost never seen the phrase “coherent quantum state” written out in mathematical physics, so I would prefer to have this long unusual name as a redirect only. Of course, we often talk about the coherence of quantum states. But this is about a general feature of coherence, like in optics. The specific states in mathematical physics which, among other features, have such coherence properties are usually called squeezed coherent states, and the coherent states of these entry are even more specific than those. I am about to add a couple of new references, so I came across the page again.

- Discussion Type
- discussion topiccoherent states > history
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Mar 11th 2021

- Discussion Type
- discussion topiccohomology operation
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by David_Corfield
- Last Active Mar 11th 2021

added a little bit of content to

*cohomology operation*

- Discussion Type
- discussion topicAndrzej Kozlowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 11th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant bundle*

- Discussion Type
- discussion topicLawvere theory
- Category Latest Changes
- Started by Urs
- Comments 43
- Last comment by Sam Staton
- Last Active Mar 11th 2021

started a Properties-section at Lawvere theory with some basic propositions.

Would be thankful if some experts looked over this.

Also added the example of the theory of sets. (A longer list of examples would be good!) And added the canonical reference.

- Discussion Type
- discussion topicequivariance group
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 11th 2021

just for completeness, to go alongside

*structure group*,*gauge group*, etc.

- Discussion Type
- discussion topicmulti-adjoint
- Category Latest Changes
- Started by Mike Shulman
- Comments 10
- Last comment by David_Corfield
- Last Active Mar 11th 2021

- Discussion Type
- discussion topicYves Diers
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Tim_Porter
- Last Active Mar 11th 2021

brief

`category:people`

-entry for hyperlinking references at*spectrum (geometry)*and at*multi-adjoint*

- Discussion Type
- discussion topiccrossed module
- Category Latest Changes
- Started by domenico_fiorenza
- Comments 12
- Last comment by Tim_Porter
- Last Active Mar 11th 2021

At crossed module it seems we are missing what i think should be the prototypical example: the relative second homotopy group $\pi_2(X,A)$ together with the bundary map $\delta:\pi_2(X,A)\to \pi_1(A)$ and the $\pi_1(A)$-action on $\pi_2(X,A)$. As someone confirms this example is correct I’ll add it to crossed module.

- Discussion Type
- discussion topicAxel Osmond
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Tim_Porter
- Last Active Mar 11th 2021

brief

`category:people`

-entry for hyperlinking references at*spectrum (geometry)*and now also at*mutli-adjoint*

- Discussion Type
- discussion topicmultireflexive subcategory
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Mar 10th 2021

- Discussion Type
- discussion topicspectrum (geometry)
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active Mar 10th 2021

- Discussion Type
- discussion topicmultilimit
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Mar 10th 2021

- Discussion Type
- discussion topicsubobject classifier
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by nLab edit announcer
- Last Active Mar 10th 2021

at subobject classifier I have cleaned up the statement of the definition and then indicated the proof that in locally small categories subobject classifiers precisely represent the subobject-presheaf.

- Discussion Type
- discussion topicfield
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by Urs
- Last Active Mar 10th 2021

I added to field a mention of some other constructive variants of the definition, with a couple more references.

- Discussion Type
- discussion topicChristopher Dwyer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 10th 2021

brief

`category:people`

-entry for hyperlinking references at*twisted equivariant K-theory*

- Discussion Type
- discussion topicValentin Zakharevich
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 10th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant K-theory*,*twisted equivariant K-theory*,*orbifold K-theory*and*Verlinde ring*

- Discussion Type
- discussion topic(g-2) anomaly
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 10th 2021

This needs an entry of its own (currently hidden in a subsection of

*anomalous magnetic moment*).Just starting something here, from my phone over coffee. More later.

- Discussion Type
- discussion topicCabibbo anomaly
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 10th 2021

this has been seen over $4\sigma$ for a while now; time to record some references and to relate to

*flavour anomaly*.Just starting here, from my phone over coffee. Nothing much to see here yet.

- Discussion Type
- discussion topiclifted limit
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Dmitri Pavlov
- Last Active Mar 10th 2021

we had

*created limit*,*reflected limit*,*preserved limit*, but not*lifted limit*. I have now created a stub for the last one, for completeness.Would be good to harmonize and cross-relate these four entries more…

- Discussion Type
- discussion topicneural network
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Richard Williamson
- Last Active Mar 9th 2021

Stub. For the moment just for providing a place to record this reference:

- Jean Thierry-Mieg,
*Connections between physics, mathematics and deep learning*, Letters in High Energy Physics, vol 2 no 3 (2019) (doi:10.31526/lhep.3.2019.110)

- Jean Thierry-Mieg,

- Discussion Type
- discussion topicJosé María Cantarero López
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 9th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant K-theory*

- Discussion Type
- discussion topicorbifold cohomology
- Category Latest Changes
- Started by Urs
- Comments 103
- Last comment by Urs
- Last Active Mar 9th 2021

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 topicBranko Juran
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 9th 2021

brief

`category:people`

-entry for hyperlinking references at*orbifold cohomology*

- Discussion Type
- discussion topicMO
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 9th 2021

added pointer to

- Sergei Novikov,
*Homotopy properties of Thom complexes*, Mat. Sbornik 57 (1962), no. 4, 407–442, 407–442 (pdf)

- Sergei Novikov,

- Discussion Type
- discussion topicrational Cohomotopy
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 9th 2021

splitting this off from

*Cohomotopy*to make room for discussion of the Sullivan models from- Jesper Møller, Martin Raussen,
*Rational Homotopy of Spaces of Maps Into Spheres and Complex Projective Spaces*, Transactions of the American Mathematical Society Vol. 292, No. 2 (Dec., 1985), pp. 721-732 (jstor:2000242)

- Jesper Møller, Martin Raussen,

- Discussion Type
- discussion topicequivariant Chern character
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 9th 2021

- Discussion Type
- discussion topicRoss Street
- Category Latest Changes
- Started by Tim_Porter
- Comments 17
- Last comment by Tim_Porter
- Last Active Mar 9th 2021

As there had been a change to the entry for Ross Street I gave it a glance. Is there a reason that the second reference is to a paper without Ross as an author?I hesitate to delete it as there may be a hidden reason. (I have edited this discussion entry to remedy the point that Todd and Urs have made below. I also edited the title of this discussion!)

- Discussion Type
- discussion topicFreed-Witten anomaly
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 8th 2021

added pointer to

- James Sparks,
*Global Worldsheet Anomalies from M-Theory*, JHEP 0408:037, 2004 (arXiv:hep-th/0310147)

on relating the Freed-Witten anomaly to the shifted C-field flux quantization

(also linked the other way around)

- James Sparks,

- Discussion Type
- discussion topicWhitehead product
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Mar 8th 2021

- Discussion Type
- discussion topicJuan Carlos Rocha Barriga
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

brief

`category:people`

-entry for hyperlinking references at*twisted differential K-theory*

- Discussion Type
- discussion topicFabio Ferrari Ruffino
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

brief

`category:people`

-entry for hyperlinking references at*twisted differential K-theory*

- Discussion Type
- discussion topictwisted differential K-theory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 8th 2021

added some lines on the relation to D-brane charge (spun off from additions I just made to

*twisted differential cohomoloy*), and added more references

- Discussion Type
- discussion topicByungdo Park
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

brief

`category:people`

-entry for hyperlinking references at*twisted differential K-theory*and at*equivariant ordinary differential cohomology*

- Discussion Type
- discussion topicNorihiro Iizuka
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

brief

`category:people`

-entry for hyperlinking references at*Witten-Sakai-Sugimoto model*and at*nuclear matrix model*

- Discussion Type
- discussion topicbrane matrix models -- content
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

- Discussion Type
- discussion topicTakeshi Morita
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

brief

`category:people`

-entry for hyperlinking references at*nuclear matrix model*

- Discussion Type
- discussion topicYoshinori Matsuo
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

brief

`category:people`

-entry for hyperlinking references at*nuclear matrix model*and elsewhere

- Discussion Type
- discussion topicnuclear matrix model
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 8th 2021

- Discussion Type
- discussion topicweak adjoint
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Mar 7th 2021

- Discussion Type
- discussion topicSimon Ross
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 7th 2021