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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics 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 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 k-theory kan lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nlab nonassociative noncommutative noncommutative-geometry number-theory object 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicgeometric theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 38
- Last comment by Urs
- Last Active Nov 24th 2021

Added a description of several different approaches to geometric theory.

- Discussion Type
- discussion topicCW-pair
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Nov 24th 2021

I gave

*CW-pair*its own entry.

- Discussion Type
- discussion topicCartan subalgebra
- Category Latest Changes
- Started by Bartek
- Comments 2
- Last comment by Bartek
- Last Active Nov 23rd 2021

- Discussion Type
- discussion topicessentially algebraic theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by anuyts
- Last Active Nov 23rd 2021

added references to

*essentially algebraic theory*. Also equipped the text with a few more hyperlinks.

- Discussion Type
- discussion topicRoman Mikhailov
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 23rd 2021

- Discussion Type
- discussion topicquantum error correction
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by Urs
- Last Active Nov 23rd 2021

- Discussion Type
- discussion topicconfinement
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by Urs
- Last Active Nov 23rd 2021

stub for

*confinement*, but nothing much there yet. Just wanted to record the last references there somewhere.

- Discussion Type
- discussion topicneutron star
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 23rd 2021

added pointer to discussion of models of neutron stars by Skyrmions:

- Carlos Naya,
*Neutron stars within the Skyrme model*, Int. J. Mod. Phys. E 28, 1930006 (2019) (arXiv:1910.01145)

- Carlos Naya,

- Discussion Type
- discussion topiccategorical model of dependent types
- Category Latest Changes
- Started by Mike Shulman
- Comments 42
- Last comment by David_Corfield
- Last Active Nov 22nd 2021

Created categorical model of dependent types, describing the various different ways to strictify category theory to match type theory and their interrelatedness. I wasn’t sure what to name this page — or even whether it should be part of some other page — but I like having all these closely related structures described in the same place.

- Discussion Type
- discussion topicworldline formalism
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Nov 22nd 2021

created

*worldline formalism*to go with this Physics.SE answer

- Discussion Type
- discussion topicinfinity-group
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Nov 22nd 2021

- Discussion Type
- discussion topicSerre subcategory
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Nov 21st 2021

- Discussion Type
- discussion topicBorel model structure
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Nov 21st 2021

- Discussion Type
- discussion topicCW-complexes are paracompact Hausdorff spaces
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 21st 2021

for completeness, I have added pointer to

- Allen Hatcher, Prop. A.3 of
*Algebraic Topology*, Cambridge University Press 2002 (ISBN:9780521795401, webpage)

for proof of the Hausdorff property of CW complexes

- Allen Hatcher, Prop. A.3 of

- Discussion Type
- discussion topicOka principle
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by David_Corfield
- Last Active Nov 20th 2021

added publication data to:

- Finnur Lárusson,
*Model structures and the Oka principle*, Journal of Pure and Applied Algebra Volume 192, Issues 1–3, 1 September 2004, Pages 203-223 (math.CV/0303355, doi:10.1016/j.jpaa.2004.02.005)

- Finnur Lárusson,

- Discussion Type
- discussion topicloop space object
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 4
- Last comment by Urs
- Last Active Nov 20th 2021

- Discussion Type
- discussion topicconvolution product of distributions
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active Nov 20th 2021

started some minimum at

*convolution product of distributions*

- Discussion Type
- discussion topiccomplex analytic ∞-groupoid
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Nov 20th 2021

added publication data for:

- Michael Hopkins, Gereon Quick,
*Hodge filtered complex bordism*, Journal of Topology,**8**1 (2015) (arXiv:1212.2173, doi:10.1112/jtopol/jtu021)

- Michael Hopkins, Gereon Quick,

- Discussion Type
- discussion topiclittle cubes operad
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Hurkyl
- Last Active Nov 19th 2021

added statement of and references to the weak equivalence with the Fulton-MacPherson operad (here)

added the same statement also at

*Fulton-MacPherson operad*

- Discussion Type
- discussion topicgeneralized universal bundle
- Category Latest Changes
- Started by Tim_Porter
- Comments 20
- Last comment by Urs
- Last Active Nov 18th 2021

Max New: at (129.10.9.38) has put a query on the generalized universal bundle entry. It says:

I don’t understand the above diagram, what is the point $* \to X$ in question? and how does this relate to the universal bundle? In particular, there is a sequence below that has a map from $\Omega_{pt} \to \mathbf{E}_{pt}$ but I don’t see how to construct that from the above.

So I think this is a typo, but I don’t know enough to correct it.

- Discussion Type
- discussion topicaxiom of replacement
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by DavidRoberts
- Last Active Nov 17th 2021

- Discussion Type
- discussion topicequicontinuous family of functions
- Category Latest Changes
- Started by Jem Lord
- Comments 1
- Last comment by Jem Lord
- Last Active Nov 17th 2021

- Discussion Type
- discussion topicbounded geometric morphism
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Nov 17th 2021

started stub for bounded geometric morphism

- Discussion Type
- discussion topicseparator
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Urs
- Last Active Nov 17th 2021

I created

*separator*, while having the nagging feeling that we already have this entry. Of course after creating it I remembered the page*generator*.So we should merge the stuff. Might this be an occasion to merge

*away*from*generator*? A set of “generating objects” also means other things than “separating objects” (notably colimit generation). So I’d be inclined to move all material to*separator*. That would also allow to drop the warning at the beginning of*generator*.

- Discussion Type
- discussion topicLie algebra object
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Nov 17th 2021

am splitting this off from

*Lie algebra*, for ease of cross-linking.

- Discussion Type
- discussion topicTôhoku
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 4
- Last comment by DavidRoberts
- Last Active Nov 17th 2021

- Discussion Type
- discussion topicleptoquark
- Category Latest Changes
- Started by Urs
- Comments 38
- Last comment by Urs
- Last Active Nov 17th 2021

- Discussion Type
- discussion topicquantum Hall effect
- Category Latest Changes
- Started by zskoda
- Comments 9
- Last comment by Urs
- Last Active Nov 17th 2021

Unfortunately, there are two entries on the same topic, both created by Urs: quantum Hall effect (redirecting also fractional quantum Hall effect what should eventually split off) with some substance, and the microstub quantum hall effect. I would like to create quantum spin Hall effect and I think I should rename/reclaim the stub quantum hall effect for this. Do others agree ? Urs ?

As the action is now delayed I record here the reference which I wanted to put there

- B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang,
*Quantum spin Hall rffect and topological phase transition in HgTe quantum wells*, Science 15 December 2006:**314**, n. 5806, pp. 1757-1761 doi

Somewhat surprisingly, the authors and roughly this work of them are mentioned (though not in the list of references) in a paper in algebraic geometry

- Ludmil Katzarkov, Ernesto Lupercio, Laurent Meersseman, Alberto Verjovsky,
*Noncommutative toric varieties*, arxiv/1308.2774

which considers the mirror symmetry and topological states of matters (topological insulators in particular) as main applications.

- B. Andrei Bernevig, Taylor L. Hughes, Shou-Cheng Zhang,

- Discussion Type
- discussion topicreal numbers object
- Category Latest Changes
- Started by Corbin
- Comments 1
- Last comment by Corbin
- Last Active Nov 16th 2021

Clean up a couple parenthetical remarks. The page ring object seems to indeed have the desired diagrams.

- Discussion Type
- discussion topicneutrino
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active Nov 16th 2021

added some comments on history to

*neutrino*.

- Discussion Type
- discussion topicKLT relations
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Nov 16th 2021

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 topicPoisson-Lie T-duality
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active Nov 16th 2021

started a bare minimum at

*Poisson-Lie T-duality*, for the moment just so as to have a place to record the two original references

- Discussion Type
- discussion topicsuperconductivity
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Nov 16th 2021

added pointer to:

- Sean Hartnoll, Andrew Lucas, Subir Sachdev, Section 6.3 of:
*Holographic quantum matter*, MIT Press 2018 (arXiv:1612.07324, publisher)

- Sean Hartnoll, Andrew Lucas, Subir Sachdev, Section 6.3 of:

- Discussion Type
- discussion topicconcordance
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Nov 16th 2021

made more explicit (here) the back-link to

*topological vector bundle*for classical concordance for topological vector bundles

- Discussion Type
- discussion topicmodel structure on diffeological spaces
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Nov 15th 2021

a stub entry, for the moment just so as to give a home to these two references:

Hiroshi Kihara,

*Model category of diffeological spaces*, Journal of Homotopy and Related Structures, (2018), 1-40 (arXiv:1605.06794)Tadayuki Haraguchi, Kazuhisa Shimakawa,

*A model structure on the category of diffeological spaces*(arXiv:1311.5668)

- Discussion Type
- discussion topicnoncommutative topology
- Category Latest Changes
- Started by jesuslop
- Comments 1
- Last comment by jesuslop
- Last Active Nov 15th 2021

- Discussion Type
- discussion topicSEAR
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Guest
- Last Active Nov 15th 2021

- Discussion Type
- discussion topicdistributive category
- Category Latest Changes
- Started by Todd_Trimble
- Comments 26
- Last comment by nLab edit announcer
- Last Active Nov 15th 2021

Spurred by an MO discussion, I added the observation that coproduct inclusions are monic in a distributive category.

- Discussion Type
- discussion topicclassifying space
- Category Latest Changes
- Started by Urs
- Comments 41
- Last comment by Urs
- Last Active Nov 15th 2021

I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.

I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.

In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes

- Discussion Type
- discussion topichierarchy problem
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by nLab edit announcer
- Last Active Nov 14th 2021

Added specific pointer to argument for solution of hierarchy problem due to Acharya-Kane-Kumar 12.

- Discussion Type
- discussion topicequivariant open cover
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 14th 2021

A stub entry, for the moment just to have a place to record

- Haibo Yang,
*Equivariant cohomology and sheaves*, Journal of Algebra,**412**2014, 230-254 (doi:10.1016/j.jalgebra.2014.05.009)

I had wanted to extract the main definition and theorem from the article into the entry, but got distracted with editing at

*good open cover*instead, and now am out of time for tonight. More later…- Haibo Yang,

- Discussion Type
- discussion topicSurj
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by David_Corfield
- Last Active Nov 14th 2021

- Discussion Type
- discussion topicPontryagin class
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Nov 14th 2021

added these pointers on the first Pontrjagin class as counting gravitational instanton number:

Tohru Eguchi, Peter Freund,

*Quantum Gravity and World Topology*, Phys. Rev. Lett. 37, 1251 (1967) (doi:10.1103/PhysRevLett.37.1251)Alexander Belavin, D. Burlankov,

*The renormalisable theory of gravitation and the einstein equations*, Physics Letters A Volume 58, Issue 1, 26 July 1976, Pages 7-8 (doi:10.1016/0375-9601(76)90530-2)

- Discussion Type
- discussion topicsemisimple Lie group
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Nov 13th 2021

- Discussion Type
- discussion topicGiraud's theorem
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by varkor
- Last Active Nov 13th 2021

added pointer to:

- Jacob Lurie,
*Giraud’s theorem*, Lecture 10 in:*Categorical Logic*, 2018 (pdf)

- Jacob Lurie,

- Discussion Type
- discussion topicinverse image
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Nov 13th 2021

- Discussion Type
- discussion topic(infinity,1)-topos
- Category Latest Changes
- Started by spitters
- Comments 8
- Last comment by Urs
- Last Active Nov 13th 2021

- Discussion Type
- discussion topicArnold-Kuiper-Massey theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by David_Corfield
- Last Active Nov 13th 2021

- Discussion Type
- discussion topicGalois connection
- Category Latest Changes
- Started by Stephan A Spahn
- Comments 4
- Last comment by David_Corfield
- Last Active Nov 12th 2021

- I added to Galois connection the remark that some authors call an adjunction between posets a *monotone Galois connection* and a dual adjunction between posets an *antitone Galois connection*.

- Discussion Type
- discussion topicmonoidal category
- Category Latest Changes
- Started by Urs
- Comments 97
- Last comment by Tim_Porter
- Last Active Nov 12th 2021

Todd,

when you see this here and have a minute, would you mind having a look at

*monoidal category*to see if you can remove the query-box discussion there and maybe replace it by some crisp statement?Thanks!

- Discussion Type
- discussion topicbicategory
- Category Latest Changes
- Started by Ahmed
- Comments 17
- Last comment by samwinnick
- Last Active Nov 11th 2021

- Discussion Type
- discussion topicgood open cover
- Category Latest Changes
- Started by Todd_Trimble
- Comments 13
- Last comment by Urs
- Last Active Nov 11th 2021

In response to an email sent to Urs by Andrew Marshall, a slight amendment to good open cover was made in the proof that paracompact manifolds admit good open covers.

- Discussion Type
- discussion topicinitial algebra of an endofunctor
- Category Latest Changes
- Started by anqurvanillapy
- Comments 4
- Last comment by jademaster
- Last Active Nov 10th 2021

- Discussion Type
- discussion topicDrinfeld center
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Nov 10th 2021

- Discussion Type
- discussion topictangle hypothesis
- Category Latest Changes
- Started by David_Corfield
- Comments 3
- Last comment by David_Corfield
- Last Active Nov 10th 2021

- Discussion Type
- discussion topicmicrocosm principle
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active Nov 10th 2021

I always found that the formulation of the theory of infinity-algebras over an (infinity,1)-operad in Lurie’s

*Higher Algebra*nicely captures what Baez-Dolan called the*microcosm principle*.I have added a corresponding remark to the latter entry and expanded slightly.

- Discussion Type
- discussion topicregular category
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Nov 10th 2021

added publication details for this reference:

- F. Cagliari, S. Mantovani, Enrico Vitale,
*Regularity of the category of Kelley spaces*, Applied Categorical Structures volume 3, pages 357–361 (1995) (doi:10.1007/BF00872904, pdf)

and am copying it over to

*compactly generated topological space*, too- F. Cagliari, S. Mantovani, Enrico Vitale,

- Discussion Type
- discussion topictopological G-space
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Urs
- Last Active Nov 10th 2021

added pointer to Bredon 72. Will add this pointer also to various related entries on equivariant homotopy theory

- Discussion Type
- discussion topicCartesian morphism
- Category Latest Changes
- Started by Hurkyl
- Comments 5
- Last comment by Hurkyl
- Last Active Nov 10th 2021

I felt like the (∞,1) section should give an abstract description rather than a model specific one, so I’ve done so, and proved in the abstract the equivalence between the hom-space and slice-category characterizations.

It feels like cheating to invoke the Grothendieck construction for it; can the argument be made just as cleanly without it?

… I’m having trouble with the formatting, so I’m going to do some bisection to track down the issue….

- Discussion Type
- discussion topic(∞,1)-algebraic theory
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Nov 9th 2021