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 book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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 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 topicSpam attack, deletion of entries
- Category Latest Changes
- Started by Tim_Porter
- Comments 14
- Last comment by Urs
- Last Active Apr 26th 2013

Look at what has been happening at derivator. The entry was erased and various things put there by an Anonymous Coward. Another one has reinstated the original one!! Has anyone noticed this? I was travelling about the time it happened so my usual check did not occur.

At triangle identities something similar had started. I have rolled back.

- Discussion Type
- discussion topicCartan-Eilenberg category
- Category Latest Changes
- Started by zskoda
- Comments 12
- Last comment by jim_stasheff
- Last Active Apr 26th 2013

A stub for Cartan-Eilenberg categories.

- Discussion Type
- discussion topichomotopy n-type - table
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Apr 25th 2013

created a table

*homotopy n-type - table*and included it into the relevant entries

- Discussion Type
- discussion topicdouble groupoid
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Apr 25th 2013

While creating

*double Lie algebroid*I notied that we had a neglected entry*double groupoid*. I gave it a few more lines.

- Discussion Type
- discussion topicWallman base, Wallman compactification
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Apr 24th 2013

Wallman compactification, redirecting also Wallman base (previously wanted at Stone Spaces). See the link to videos by Caramello, where also Alain Connes participates in a discussion.

- Discussion Type
- discussion topicnoncommutative stable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 24th 2013

I felt we needed an entry explicitly titled

*noncommutative stable homotopy theory*. So I created one. But it’s just a glorified redirect to*KK-theory*and*E-theory*.

- Discussion Type
- discussion topicsymplectic leaf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 23rd 2013

added references to

*symplectic leaf*

- Discussion Type
- discussion topicscattering theory
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by zskoda
- Last Active Apr 22nd 2013

New stubs scattering and abstract scattering theory.

- Discussion Type
- discussion topicChevalley's theorem on constructible sets
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by Urs
- Last Active Apr 18th 2013

Chevalley’s theorem on constructible sets and elimination of quantifiers. The entries are related ! The interest came partly from teaching some classical algebraic geometry these days. The related entry is also forking, though yet it is not said why; non-forking may be viewed as related to a notion of generic point, generic type (in the sense of model theory).

- Discussion Type
- discussion topicPlack Collaboration
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by Urs
- Last Active Apr 18th 2013

Was this meant to be Planck Collaboration? I have renamed it!

- Discussion Type
- discussion topiclocally closed set
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Todd_Trimble
- Last Active Apr 18th 2013

- Discussion Type
- discussion topicrational map, variety etc.
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Apr 18th 2013

To add the old entry birational geometry I added a number of classical, very geometric, algebraic geometry entries rational map, birational map, rational variety, image of a rational map, unirational variety and a number of redirects. The notion of an image is a bit unusual because the varieties and rational maps do not make a category, as the composition is not always defined. However the notion of the image is still very natural here. For the concept of dominant rational map I did not make a separate entry but discussed it within rational map and made redirects.

- Discussion Type
- discussion topicHopf algebroid over a commutative base
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Apr 18th 2013

I moved much of material from Hopf algebroid to Hopf algebroid over a commutative base, where both groupoid convolution algebras and group function algebras belong there. Most of the difference is seen already at the level of bialgebroid, the stuff about antipode in general case is to be written. Some more changes to both entries.

- Discussion Type
- discussion topicmetric abstract elementary class
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Apr 18th 2013

A stub for metric abstract elementary class. Related changes/additions on some model theory entries like elementary class of structures, forking entered a related blog at math blogs.

- Discussion Type
- discussion topiccofinal (oo,1)-functor
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 18th 2013

created cofinal (infinity,1)-functor

- Discussion Type
- discussion topicslice-(infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 18th 2013

added to

*slice (infinity,1)-category*the statement that projecting slicing object away (dependent sum) reflects $\infty$-colomits.

- Discussion Type
- discussion topicMaps
- Category Latest Changes
- Started by TobyBartels
- Comments 5
- Last comment by TobyBartels
- Last Active Apr 17th 2013

For some reason, we never had map redirect to function, but now we do. Same with mapping.

This may or may not be the best behaviour. We might actually want a page on how people distinguish these words, such as in topology (‘map’ = continuous map but ‘function’ = function, maybe).

- Discussion Type
- discussion topicfield (physics)
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active Apr 17th 2013

started

*field (physics)*.So far there is an Idea-section, a general definition with some remarks, and the beginning of a list of examples, which after the first spelled out (gravity) becomes just a list of keywords for the moment.

More later.

- Discussion Type
- discussion topicA-infinity category
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by DavidRoberts
- Last Active Apr 16th 2013

Added to

*A-infinity category*the references pointed to by Bruno Valette here.

- Discussion Type
- discussion topicBinary Golay code
- Category Latest Changes
- Started by DavidRoberts
- Comments 3
- Last comment by DavidRoberts
- Last Active Apr 15th 2013

Created binary Golay code. The construction is a little involved, and I haven’t put it in yet, because I think I can nut out a nicer description. The construction I aim to describe, in slightly different notation and terminology is in

R. T. Curtis (1976). A new combinatorial approach to M24. Mathematical Proceedings of the Cambridge Philosophical Society, 79, pp 25-42. doi:10.1017/S0305004100052075.

- Discussion Type
- discussion topickinematic tangent bundle
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Apr 15th 2013

I noticed that we have

*kinematic tangent bundle*.To incorporate this a bit into the nLab -web I have created stubs for

*operational tangent bundle*(wanted by its kinematic cousin) and for*synthetic tangent bundle*and then I have interlinked all these entries and linked to them from*tangent bundle*.Also gave the Idea-section of

*kinematic tangent bundle*a very first paragraph which very briefly says it all, before diving into discussion of what generalized smooth spaces are etc.

- Discussion Type
- discussion topicvanishing at infinity
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by TobyBartels
- Last Active Apr 15th 2013

- Discussion Type
- discussion topichomotopical structure on C*-algebras
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Apr 11th 2013

created

*homotopical structure on C*-algebras*, summarized some central statements from Uuye’s article on structure of categories of fibrant objects on $C^\ast Alg$.

- Discussion Type
- discussion topicCategorical Homotopy Theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 10th 2013

added to some relevant entries a pointer to

- Emily Riehl,
*Categorical homotopy theory*, Lecture notes (pdf)

- Emily Riehl,

- Discussion Type
- discussion topicE-theory
- Category Latest Changes
- Started by zskoda
- Comments 6
- Last comment by Urs
- Last Active Apr 10th 2013

There is a new stub E-theory with redirect asymptotic morphism, new entry semiprojective morphism (of separable $C^\ast$-algebras) and stub Brown–Douglas–Fillmore theory, together with some recent bibliography&links changes at Marius Dadarlat, shape theory etc. There should be soon a separate entry shape theory for operator algebras but I still did not do it.

- Discussion Type
- discussion topicasymptotic C*-homomorphism
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 10th 2013

- Discussion Type
- discussion topictrialgebra and Hopf monoidal category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 9th 2013

created entries

*trialgebra*and*Hopf monoidal category*also expanded the Tannaka-duality overview table (being included in related entries):

to contain the first entries of the corresponding “higher Tannaka duality” relations

- Discussion Type
- discussion topichopfish algebra
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Urs
- Last Active Apr 9th 2013

- Discussion Type
- discussion topicHilbert bimodule
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 9th 2013

added to

*Hilbert bimodule*a pointer to the Buss-Zhu-Meyer article on their tensor products and induced 2-category structure.

- Discussion Type
- discussion topicrelative categories
- Category Latest Changes
- Started by Zhen Lin
- Comments 1
- Last comment by Zhen Lin
- Last Active Apr 8th 2013

I have now created relative category.

Question: Does the transferred model structure on $\mathbf{RelCat}$ resolve Rezk’s [2001] conjecture that the classification diagram of a model category is weakly equivalent to its simplicial localisation? The $N_\xi$ functor looks very close to computing the hammock localisation to me…

- Discussion Type
- discussion topicweak Hopf algebra
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 8th 2013

cross-linked

*weak Hopf algebra*and*fusion category*a bit more explicitly, added to both a reference to Ostrik’s article that shows the duality and added a corresponding item to

- Discussion Type
- discussion topichigher groupoid C*-algebras
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 8th 2013

I have added to

*groupoid convolution algebra*the beginning of an Examples-section titled*Higher groupoid convolution algebras and n-vector spaces/n-modules*.Conservatively, you can regard this indeed as just some examples of applications of the groupoid convolution algebra construction. But the way it is presented is supposed to be suggestive of a “higher C*-algebra” version of convolution algebras of higher Lie groupoids.

I have labelled it as “under construction” to reflect the fact that this latter aspect is a bit experimental for the moment.

The basic idea is that to the extent that we do have groupoid convolution as a (2,1)-functor

$C \colon Grpd \to Alg_{b}^{op} \simeq 2Mod$(as do do for discrete geometry and conjecturally do for smooth geometry), then this immediately means that it sends double groupoids to convolution sesquialgebras, hence to 3-modules with basis (3-vector spaces).

As the simplest but instructive example of this I have spelled out how the ordinary dual(commutative and non-co-commutative) Hopf algebra of a finite group arises this way as the “horizontally constant” double groupoid incarnation of $\mathbf{B}G$, while the convolution algebra of $G$ is the algebra of the “vertically discrete” double groupoid incarnation of $\mathbf{B}G$.

But next, if we simply replace the bare $Alg_b^{op} \simeq 2 Mod$ with the 2-category $C^\ast Alg_b$ of $C^\ast$-algebras and Hilbert bimodules between them and assume (as seems to be the case) that $C^\ast$-algebraic groupoid convolution is a 2-functor

$LieGrpd_{\simeq} \to C^\ast Alg_n^{op}$then the same argument goes through as before and yields convolution “$C^\ast$-2-algebras” that look like Hopf-C*-algebras. Etc. Seems to go in the right direction…

- Discussion Type
- discussion topiccohomological integration
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 7th 2013

seeing the announcement of that diffiety summer school made me think that we should have a dedicated entry titled

*cohomological integration*which points to the aspects of this discussed already elswhere on the nLab, and which eventually lists dedicated references, if any. So I created a stub.Does anyone know if there is a published reference to go with the relevant diffiety-school page ?

- Discussion Type
- discussion topicbibundle
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Apr 5th 2013

dropped some lines into a new Properties-section in the old and neglected entry

*bibundle*. But not for public consumption yet.

- Discussion Type
- discussion topicclosure operator
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active Apr 4th 2013

I felt we were lacking an entry

*closure operator*. I have started one, but don’t have more time now. It’s left in a somewhat sad incomplete state for the moment.

- Discussion Type
- discussion topicclassification of finite groups
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by zskoda
- Last Active Apr 4th 2013

just noticed that this morning some apparently knowledgable person signing as “Snoyle” added two paragraphs to finite group with technical details.

I have helped a bit with the syntax now and split off entries for quasisimple group and generalized Fitting subgroup

- Discussion Type
- discussion topicHopf C-star-algebra
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Apr 2nd 2013

started

*Hopf C-star algebra*(but my computer is running out of battery power now..)

- Discussion Type
- discussion topiccanonical Hilbert-space of half-densities
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 1st 2013

brief note:

*canonical Hilbert space of half-densities*

- Discussion Type
- discussion topicstar-algebras and dagger-categories
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Apr 1st 2013

Added brief comments at

*star algebra*, at*dagger category*and at*category algebra*on how convolution algebras on dagger-categories are naturally star algebras.

- Discussion Type
- discussion topicTannakian category
- Category Latest Changes
- Started by adeelkh
- Comments 5
- Last comment by Tim_Porter
- Last Active Apr 1st 2013

I made a stub Tannakian category with some references.

- Discussion Type
- discussion topicLanglands dual groups and T-duality
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 31st 2013

Added the recent reference on Langlands dual groups as T-dual groups to both

*geometric Langlands correspondence*and*T-duality*together with a brief sentence. But nothing more as of yet.

- Discussion Type
- discussion topictopological algebra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 31st 2013

I could have sworn that we already had entries like “topological ring”, “topological algebra” or the like. But maybe we don’t, or maybe I am looking for the wrong variant titles.

I ended up creating a stub for topological algebra now…

- Discussion Type
- discussion topicC-star algebra
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Mar 31st 2013

I have added to C-star algebra the statement that the image of a $C^\ast$-algebra under an $\ast$-homomorphism is again $C^\ast$.

Also reorganized the Properties-section a bit and added more references.

- Discussion Type
- discussion topicEpsilons, epsilons, everywhere epsilons
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by TobyBartels
- Last Active Mar 30th 2013

- Discussion Type
- discussion topicgroupoid
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by David_Corfield
- Last Active Mar 29th 2013

the entry

*groupoid*could do with some beautifying.I have added the following introductory reference:

- Alan Weinstein,
*Groupoids: Unifying Internal and External Symmetry – A Tour through some Examples*, Notices of the AMS volume 43, Number 7 (pdf)

- Alan Weinstein,

- Discussion Type
- discussion topicmodules over Lie groupoid convolution algebras
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 29th 2013

I have started adding some references to

on modules ($C^\ast$-modules) of (continuous, etc..) convolution algebras of topological/Lie groupoids.

I still need to look into this more closely. A motivating question for this kind of thing is:

what’s the right fine-tuning of the definition of modules over twisted Lie groupoid convolution algebras such that for centrally extended Lie groupoids it becomes equivalent to the corresponding gerbe modules?

This seems fairly straightforward, but there are is some technical fine-tuning to deal with. I was hoping this is already stated cleanly in the literature somewhere. But maybe it is not. Or maybe I just haven’t seen it yet.

- Discussion Type
- discussion topiccentrally extended groupoid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 29th 2013

Wrote a quick note at

*centrally extended groupoid*and interlinked a little, for the moment just motivated by having the link point somwhere.

- Discussion Type
- discussion topicGoldblatt-Thomason theorem
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by Tim_Porter
- Last Active Mar 29th 2013

- Discussion Type
- discussion topicfoliation of a Lie groupoid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 25th 2013

- Discussion Type
- discussion topicLie algebroid-groupoid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 25th 2013

- Discussion Type
- discussion topicfoliation of a Lie algebroid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 25th 2013

am starting

*foliation of a Lie algebroid*

- Discussion Type
- discussion topicdouble Lie algebroid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 25th 2013

stub for

*double Lie algebroid*

- Discussion Type
- discussion topicpolarization
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by crogers
- Last Active Mar 22nd 2013

as mentioned in another thread, I have expanded the Idea-section at

*polarization*in order to highlight the relation to*canonical momenta*(which I also edited accordingly).

- Discussion Type
- discussion topicPositive numbers
- Category Latest Changes
- Started by TobyBartels
- Comments 1
- Last comment by TobyBartels
- Last Active Mar 22nd 2013

I keep making links to positive number, so now I filled them.

- Discussion Type
- discussion topicphase and phase space in physics
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 22nd 2013

felt like making a terminological note on

*phase and phase space in physics*(and linked to it from the relevant entries).If anyone has more information on the historical origin of the term “phase space”, please let me know.

- Discussion Type
- discussion topicphase
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by TobyBartels
- Last Active Mar 22nd 2013

started a dismabiguation page for

*phase*. Feel invited to add further meanings.

- Discussion Type
- discussion topicCauchy's mistake
- Category Latest Changes
- Started by TobyBartels
- Comments 17
- Last comment by TobyBartels
- Last Active Mar 22nd 2013

- Discussion Type
- discussion topicsemiclassical state
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 21st 2013

Just in case you see me editing in the

*Recently Revised*list and are wondering:I have created and have started to fill some content into

*semiclassical state*. But I am not done yet and the entry is not in good shape yet. So don’t look at yet it unless in a mood for fiddling and editing.

- Discussion Type
- discussion topicclassical-to-quantum notions - table
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 21st 2013

I started an entry

*classical-to-quantum notions - table*for inclusion in “Related concepts”-sections in the relevant entries.This is meant to clean up the existing such “Related concepts”-lists. But I am not done yet with the cleaning-up…

- Discussion Type
- discussion topicsemiclassical+approximation
- Category Latest Changes
- Started by zskoda
- Comments 10
- Last comment by Urs
- Last Active Mar 21st 2013

New entry semiclassical approximation. It requires a careful choice of references. The ones at the wikipedia article are catastrophically particular, 1-dimensional, old and non-geometric and hide the story more than reveal. Stub Maslov index containing the main references for Maslov index.