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- Discussion Type
- discussion topicG2-conifold
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 14th 2020

- Discussion Type
- discussion topicG2-conifolds -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 14th 2020

starting something (a bare list of references, to be

`!include`

ed into relevant entries, such as at*G2-manifold*and*conical singularity*)

- Discussion Type
- discussion topiccone (Riemannian geometry)
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 14th 2020

- Discussion Type
- discussion topicmetric cone over complex projective 3-space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 14th 2020

- Discussion Type
- discussion topicquark-gluon plasma
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Oct 14th 2020

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 topicchord diagram
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 9
- Last comment by Urs
- Last Active Oct 14th 2020

I created a short page for chord diagram, and also added a bit of relevant information to Vassiliev invariant.

- Discussion Type
- discussion topicsemi-abelian category
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Oct 13th 2020

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 topicflavor on heterotic M5-branes -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 13th 2020

a bare list of references, to be

`!include`

-ed into the References-sections of relevant entries (such as*flavor (particle physics)*)

- Discussion Type
- discussion topicname binding
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 13th 2020

a stub, to satisfy links at

*Schanuel topos*

- Discussion Type
- discussion topicopen problem of confinement -- references
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Oct 13th 2020

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 topicConnes-Lott-Chamseddine-Barrett model
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Oct 13th 2020

I finally gave the

*Connes-Lott-Chamseddine-Barrett model*its own entry. So far it contains just a minimum of an Idea-section and a minimum of references.This was prompted by an exposition on

*PhysicsForums Insights*that I wrote:*Spectral standard model and String compactifications*

- Discussion Type
- discussion topicquantum decoherence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 13th 2020

added pointer to today’s

- Chris Nagele, Oliver Janssen, Matthew Kleban,
*Decoherence: A Numerical Study*(arXiv:2010.04803)

- Chris Nagele, Oliver Janssen, Matthew Kleban,

- Discussion Type
- discussion topicScience of Logic
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active Oct 13th 2020

added English translation of this bit

PN§260 Der Raum ist in sich selbst der Widerspruch des gleichgültigen Auseinanderseins und der unterschiedlosen Kontinuität, die reine Negativität seiner selbst und das Übergehen zunächst in die Zeit. Ebenso ist die Zeit, da deren in Eins zusammengehaltene entgegengesetzte Momente sich unmittelbar aufheben, das unmittelbare Zusammenfallen in die Indifferenz, in das ununterschiedene Außereinander oder den Raum.

Space is in itself the contradiction of the indifferent being-apart and of the difference-less continuity, the pure negativity of itself and the transformation, first of all, to time. In the same manner time – since its opposite moments, held together in unity, immeditely sublate themselves – is the undifferentiated being-apart or: space.

And polished a little around and following this bit.

- Discussion Type
- discussion topicinfinitesimal interval object
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Dean
- Last Active Oct 12th 2020

I have typed into infinitesimal interval object a detailed description of the simplicial object inuced on a microlinear space from the infinitesimal interval in immediate analogy to the construction of the finite path simplicial object induced from an interval object (as discussed there).

I also give the inclusion of the infinitesimal simplicial object into the finite one.

All the proofs here are straightforward checking, which I think I have done rather carefully on paper, but not typed up. What I would appreciate, though, is if somebody gave me a sanity check on the definition of the infinitesimal simplicial object (which is typed in detail).

In the very last section, which is the one that is still just a sketch, I am hoping to describe an isomorphism from my simplicial infinitesimal object to that considered by Anders Kock, which is currently described at infinitesimal singular simplicial complex in the case that the space X satisfies Kock's assumptions (it must be a "formal manifold").

The construction I discuss at infinitesimal interval object is supposed to generalize Kock's construction to all microlinear spaces and motivated by having that canonical obvious inclusion into the finite version at interval object.

The isomorphism should be evident: my construction evidently yields in degree k k-tuples of pairwise first oder neighbours if the space X admits that notion. But I want to sleep over this statement one more night...

- Discussion Type
- discussion topicbitopological space
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 5
- Last comment by Dmitri Pavlov
- Last Active Oct 12th 2020

- Discussion Type
- discussion topicShiing-shen Chern
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 12th 2020

added this second-order-quote:

Chen Ning Yang writes in

*C. N. Yang, Selected papers, 1945-1980, with commentary*, W. H. Freeman and Company, San Francisco, 1983, on p. 567:In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”

- Discussion Type
- discussion topicChen Ning Yang
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Oct 12th 2020

added these two quotes:

Yang wrote in

*C. N. Yang, Selected papers, 1945-1980, with commentary*, W. H. Freeman and Company, San Francisco, 1983, on p. 567:In 1975, impressed with the fact that gauge fields are connections on fiber bundles, I drove to the house of S. S. Chern in El Cerrito, near Berkeley… I said I found it amazing that gauge theory are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added: “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.

Yang expanded on this passage in an interview recorded as:

*C. N. Yang and contemporary mathematics*, chapter in: Robin Wilson, Jeremy Gray (eds.),*Mathematical Conversations: Selections from The Mathematical Intelligencer*, Springer 2001, on p. 72 (GoogleBooks):But it was not just joy. There was something more, something deeper: After all, what could be more mysterious, what could be more awe-inspiring, than to find that the structure of the physical world is intimately tied to the deep mathematical concepts, concepts which were developed out of considerations rooted only in logic and the beauty of form?

- Discussion Type
- discussion topicequivariant Sullivan model
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 12th 2020

- Discussion Type
- discussion topicdelocalized equivariant cohomology
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active Oct 12th 2020

- Discussion Type
- discussion topicnatural homotopy
- Category Latest Changes
- Started by Thomas Holder
- Comments 3
- Last comment by Thomas Holder
- Last Active Oct 12th 2020

- Discussion Type
- discussion topicincarnations of rational equivariant topological K-theory -- table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 12th 2020

- Discussion Type
- discussion topicD1-D5 brane bound state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 12th 2020

added pointer to today’s

- Daniel R. Mayerson, Masaki Shigemori,
*Counting D1-D5-P Microstates in Supergravity*(arXiv:2010.04172)

- Daniel R. Mayerson, Masaki Shigemori,

- Discussion Type
- discussion topicequivariant Chern character
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Oct 11th 2020

- Discussion Type
- discussion topiccompositionality
- Category Latest Changes
- Started by David_Corfield
- Comments 28
- Last comment by Richard Williamson
- Last Active Oct 11th 2020

- Discussion Type
- discussion topicinhabited object
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Oct 11th 2020

I split off inhabited object from inhabited set.

(moved Mike's and Toby's old discussion query box to the new entry, too)

I added an Examples section with a remark about this issue in the context of Models for Smooth Infinitesimal Analysis, that I happen to be looking into.

personally, I feel I need more examples still at internal logic to follow this in its full scope. I guess I should read the Elephant one day, finally.

In the book Moerdijk-Reyes say in a somewhat pedestrian way that existential quantifiers in the internal logic of a sheaf topos are to be evaluated on covers, hence asking internally if a sheaf has a (internally global) element means asking if for any cover of the point, there is a morphism .

That's fine with me and I follow this in as far as the purpose of their book is concerned, but I need to get a better idea of how the logical quantifiers are formulate in internal logic in full generality.

- Discussion Type
- discussion topicHurewicz cofibration
- Category Latest Changes
- Started by DavidRoberts
- Comments 2
- Last comment by Tim_Porter
- Last Active Oct 11th 2020

Gave proper reference for (Kieboom 1987).

- Discussion Type
- discussion topicNuPRL
- Category Latest Changes
- Started by atmacen
- Comments 3
- Last comment by atmacen
- Last Active Oct 10th 2020

- Discussion Type
- discussion topicgeometric morphism
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Oct 10th 2020

at geometric morphism in the new section Structure preserved by geometric morphisms I wanted to expand on Johnstone’s remark B2.2.7 on how geometric morphisms preserve the characteristic well-powerdness of toposes as indexed categories over themselves. I have started at indexed category a section on well-poweredness for that purpose, but I have to leave things in very incomplete form for the moment.

- Discussion Type
- discussion topiccombinatorial functor
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 10th 2020

a stub, to make links at

*Schanuel topos*work.

- Discussion Type
- discussion topicNoam Chomsky
- Category Latest Changes
- Started by alexis.toumi
- Comments 4
- Last comment by Thomas Holder
- Last Active Oct 10th 2020