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- Discussion Type
- discussion topicmeasure space
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Dmitri Pavlov
- Last Active Jul 15th 2019

added to measure space a link to measurable locale.

In the course I notice the following remnant discussion, which hereby I move from there to here

Eric: Some day this should hopefully tie into the beautiful stuff on Leinster measure (blog).

+– {: .query} Eric: $d$ is also the exterior derivative and $d\mu$ is a volume form. Is there a nice way to say this that is consistent with the above? Update: The Usenet discussion probably discusses this, but I’m too lazy to read the whole thing right now (past my bedtime!).

*Toby*: As a volume form is not, in general, the exterior derivative of anything, you cannot interpret the ‘$\mathrm{d}$’ in (eq:excessive) as an exterior derivative. You can do this for the ‘$\mathrm{d}$’ in (eq:Leibniz), of course, because that is on the real line, where the volume form*is*the exterior derivative of the identity function $(x \mapsto x)$. But in general, an absolutely continuous Radon measure $\mu$ on an oriented smooth $n$-dimensional manifold $X$ defines an $n$-form on $X$ (and vice versa), so if you call the form $\mu$ as well, then you want to use (eq:simple). (The exterior deriviative of the volume form, of course, would be zero!)I'm actually halfway through writing an article differential form where I will address some of this. (I guess that I'm going through old Usenet posts of mine; I am using the conversation that you and I had with John in this old thread as reference for some of it!)

Eric: I look forward to it! By the way, that Usenet discussion was a nice blast from the past :)

Eric: I put some comments about that discussion here.

*Toby*: I should note that, even given what I wrote above, there is still a*slight*clash of notation between measure theory and differential topology. To fix this, the $\mathrm{d}x$ in (eq:full) could be replaced with $|\mathrm{d}x|$. This has to do with the whole the-absolute-value-of-an-$n$form-is-an-$n$pseudoform and integration-of-$n$pseudoforms-is-more-fundamental-than-integration-of-$n$forms issue. I referred to this clash of notation in our Usenet conversation here.Eric: It’s starting to come back to me now. Yeah, the

*measure*is really a pseudo $n$-form and we settled on the notation $|dx|$ for that. We should at least give a nod to that idea I think in the above.

- Discussion Type
- discussion topiclocalisation of a commutative ring away from an element
- Category Latest Changes
- Started by Richard Williamson
- Comments 9
- Last comment by Dmitri Pavlov
- Last Active Jul 15th 2019

Gave an explicit definition as the quotient ring $A[x] / (ax - 1)$, and mentioned the equivalent definition in terms of multiplicative systems. Gave the example of Laurent polynomials. The explicit definition was already given at localisation of a commutative ring, but the multiplicative system was not given, and I think the construction is fundamental enough to warrant its own page. I will tweak localisation of a commutative ring to link to the new page.

- Discussion Type
- discussion topicM-theory on S1/G_HW times H/G_ADE
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 15th 2019

- Discussion Type
- discussion topicdcpo
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jul 15th 2019

- Discussion Type
- discussion topicflavour anomaly
- Category Latest Changes
- Started by Urs
- Comments 83
- Last comment by Urs
- Last Active Jul 15th 2019

- Discussion Type
- discussion topicMSSM
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 15th 2019

added pointer to

- Stefano Frixione, Benjamin Fuks, Valentin Hirschi, Kentarou Mawatari, Hua-Sheng Shao, Marthijn P. A. Sunder, Marco Zaro,
*Automated simulations beyond the Standard Model: supersymmetry*(arXiv:1907.04898)

- Stefano Frixione, Benjamin Fuks, Valentin Hirschi, Kentarou Mawatari, Hua-Sheng Shao, Marthijn P. A. Sunder, Marco Zaro,

- Discussion Type
- discussion topicdecidable object
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 15th 2019

added hyperlinks, formatting, toc.

Somebody should create an entry for

*decidable set*

- Discussion Type
- discussion topiccomplemented subobject
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 15th 2019

Added formatting, hyperlinks, toc and floating-toc.

But mainly I came here to see if

*decidable inclusion*should redirect here (which is now required at*constructive model structure on simplicial sets*). I have made it a redirect, but there is much room in this and related entries for experts to live out their expertise

- Discussion Type
- discussion topicconstructive model structure on simplicial sets
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jul 15th 2019

started a minimum, so far just in order to give a home to today’s

- Nicola Gambino, Christian Sattler, Karol Szumiło,
*The constructive Kan-Quillen model structure: two new proofs*(arXiv:1907.05394)

- Nicola Gambino, Christian Sattler, Karol Szumiło,

- Discussion Type
- discussion topichypergraph category
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by Urs
- Last Active Jul 15th 2019

Created hypergraph category.

- Discussion Type
- discussion topicintegral transforms on sheaves
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by jesuslop
- Last Active Jul 14th 2019

I am writing an exposition (or a dictionary) integral transforms on sheaves.

Check it out. I will have to go offline soon. Maybe somebody feels like further polishing/expanding this up a bit. Then later I want to supply that for the current $n$Café discussion.

- Discussion Type
- discussion topiclattice gauge theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 6
- Last comment by Urs
- Last Active Jul 13th 2019

- Discussion Type
- discussion topictwisted tensor product
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Jul 13th 2019

- Discussion Type
- discussion topicYoneda lemma
- Category Latest Changes
- Started by Urs
- Comments 97
- Last comment by Richard Williamson
- Last Active Jul 13th 2019

Todd,

you added to Yoneda lemma the sentence

In brief, the principle is that the identity morphism $id_x: x \to x$ is the universal generalized element of $x$. This simple principle is surprisingly pervasive throughout category theory.

Maybe it would be good to expand on that. One might think that the universal property of a genralized element is that every other one factors through it uniquely. That this is true for the generalized element $id_x$ is a tautological statement that does not need or imply the Yoneda lemma, it seems.

- Discussion Type
- discussion topicsimplicial map
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 12th 2019

a minimum, in order to satisfy a link that got demanded at

*constructive model structure on simplicial sets*

- Discussion Type
- discussion topicD=4 supergravity
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 12th 2019

- Discussion Type
- discussion topicDavid Spivak
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Jul 12th 2019

- Discussion Type
- discussion topicBrendan Fong
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 12th 2019

brief

`category:people`

-entry for hyperlinking references at*hypergraph category*

- Discussion Type
- discussion topicArtin gluing
- Category Latest Changes
- Started by Todd_Trimble
- Comments 10
- Last comment by Thomas Holder
- Last Active Jul 12th 2019

Some stuff that Zoran wrote on recollement reminded me that I had been long meaning to write Artin gluing, which I’ve done, starting in a kind of pedestrian way (just with topological spaces). Somewhere in the section on the topos case I mention a result to be found in the Elephant which I couldn’t quite find; if you know where it is, please let me know.

- Discussion Type
- discussion topicKlaus Heiner Kamps
- Category Latest Changes
- Started by Marc
- Comments 4
- Last comment by Tim_Porter
- Last Active Jul 12th 2019

- Discussion Type
- discussion topiccomposite Higgs model
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jul 12th 2019

a stub, on occasion of today’s

- Oliver Witzel,
*Review on Composite Higgs Models*(arXiv:1901.08216)

and to provide the previously missing link at

*flavour anomaly*for- David Marzocca,
*Addressing the B-physics anomalies in a fundamental Composite Higgs Model*, JHEP07(2018)121 (arXiv:1803.10972)

- Oliver Witzel,

- Discussion Type
- discussion topiccpo
- Category Latest Changes
- Started by Mike Shulman
- Comments 4
- Last comment by Mike Shulman
- Last Active Jul 11th 2019

I’m not sure that the definition on this page is correct. Despite how wrong it seems to a category theorist, I think the adjective “complete” in “cpo” usually refers only to a

*countable*sort of completeness. According to wikipedia, a “cpo” can mean at least three different things dependent on context, but “never” a partial order that’s actually complete as a category (i.e. a complete lattice).

- Discussion Type
- discussion topicD=6 super Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 11th 2019

- Discussion Type
- discussion topicgravitational wave
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Jul 11th 2019

just to make links work, I have started a minimum at

*gravitational wave*.

- Discussion Type
- discussion topicD=5 supergravity
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 11th 2019

- Discussion Type
- discussion topicstring theory results applied elsewhere
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Jul 11th 2019

Reading the blog entry

- Matthew Strassler,
*From string theory to the large hadron collider*(blog post)

and the reactions to it made me realize that apparently there is no comprehensive list either in print or online of all the insights into QFT in general and observed standard model physics in particular, that have been obtained via results in string theory.

So I have entertained myself with starting to collect notes for such a list:

In the process I have created a bunch of new entries, most of them stubs, linked to from there.

- Matthew Strassler,

- Discussion Type
- discussion topicKLT relations
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 11th 2019

at

*KLT relations*I have expanded the list of references. I added also references for the generalization of these relations that is known these days as “gravity is Yang-Mills squared” or similar (eventually this might want to be a separate entry).In this course I also expanded the list of references at quantum gravity – As a perturbative quantum field theory

- Discussion Type
- discussion topicDarin Morrison
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jul 11th 2019

- Discussion Type
- discussion topicaugmented simplicial set
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by atmacen
- Last Active Jul 10th 2019

I noticed that augmented simplicial set did not point anywhere, so i created the entry. But have no energy to put anything of substance there right now.

- Discussion Type
- discussion topicKilling spinor
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jul 10th 2019

added pointer to

- Ulf Gran, George Papadopoulos, Diederik Roest,
*Supersymmetric heterotic string backgrounds*, Phys.Lett.B656:119-126, 2007 (arXiv:0706.4407)

and re-arranged the references slightly, moving those on supersymmetry to a dedicated subsection

- Ulf Gran, George Papadopoulos, Diederik Roest,