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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 k-theory lie-theory 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 nforum 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 sheaves 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

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- Discussion Type
- discussion topicfield
- Category Latest Changes
- Started by Mike Shulman
- Comments 16
- Last comment by Ashley
- Last Active 8 hours ago

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

- Discussion Type
- discussion topicFourier-Laplace transform
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Anisomorphism
- Last Active 9 hours ago

just so that hyperlinks work, I created stubs for

*Fourier-Laplace transform*and also*Laplace transform*

- Discussion Type
- discussion topicunivalence axiom
- Category Latest Changes
- Started by spitters
- Comments 47
- Last comment by Ashley
- Last Active 10 hours ago

- Discussion Type
- discussion topicRiemannian immersion
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 11 hours ago

starting something on isometric immersions

— mainly I was trying to track down a reference that would clearly state that orthonormal “adapted” or “Darboux” (co)frames (here) always exist locally for an immersion into a Riemannian manifold.

What I found so far is

Mastrolia, Rigoli & Setti 2012, p. 33, where this is claimed, but just in passing

and

Chen & Giron 2021, Thm. 2.2, where this is stated in the generality of sequences of immersions, which makes it hard to recognize the simple statement behind all the analytic fine-print.

- Discussion Type
- discussion topicharmonic map
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 11 hours ago

created a bare minimum at

*harmonic map*(for the moment just so as to have a place to record the reference given there)

- Discussion Type
- discussion topicunit of an adjunction
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 12 hours ago

The entry

*unit of an adjunction*had a big chunk of mixed itex+svg code at the beginning to display an adjunction. On my machine though the output of that code was ill typeset. So I have removed the code and replaced it by plain iTex encoding of an adjunction.(Just in case anyone deeply cares about the svg that was there. It’s still in the history. If it is preferred by anyone, it needs to be fixed first.)

- Discussion Type
- discussion topiccoextension of scalars
- Category Latest Changes
- Started by John Baez
- Comments 3
- Last comment by zskoda
- Last Active 14 hours ago

- Discussion Type
- discussion topicSketches of an Elephant
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active 22 hours ago

- Discussion Type
- discussion topicAdS-QCD correspondence
- Category Latest Changes
- Started by Urs
- Comments 94
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topictopological crystalline insulator
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 1 day ago

- Discussion Type
- discussion topiczeta function of a Riemann surface
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by jesuslop
- Last Active 1 day ago

In some thread here (which I seem to have lost) there was the open question of whether the Selberg zeta function is indeed the zeta function of the corresponding Laplace operator. The answer is of course Yes, I have added the following paragraph to

*zeta function of a Riemann surface*:That the Selberg zeta function is indeed proportional to the zeta function of a Laplace operator is due to (D’Hoker-Phong 86, Sarnak 87), and that it is similarly related to the eta function of a Dirac operator on the given Riemann surface/hyperbolic manifold goes back to (Milson 78), with further development including (Park 01). For review of the literature on this relation see also the beginning of (Friedman 06).

(the links will only work from within the entry)

- Discussion Type
- discussion topicdefinitional isomorphism
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by rbocquet2
- Last Active 1 day ago

- Discussion Type
- discussion topicMichael Rathjen
- Category Latest Changes
- Started by NikolajK
- Comments 2
- Last comment by Tim_Porter
- Last Active 2 days ago

- Discussion Type
- discussion topicJoão Faria Martins
- Category Latest Changes
- Started by Tim_Porter
- Comments 6
- Last comment by Tim_Porter
- Last Active 2 days ago

- Discussion Type
- discussion topicpolar decomposition
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicGauss decomposition
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicLU decomposition
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicQR decomposition
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

a stub entry, for the moment just to satisfy links at

*matrix decomposition*and at*Gram-Schmidt process*

- Discussion Type
- discussion topicmatrix decomposition
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicGram-Schmidt process
- Category Latest Changes
- Started by Todd_Trimble
- Comments 28
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicquantum determinant
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 2 days ago

- Discussion Type
- discussion topicequivariant homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 33
- Last comment by Urs
- Last Active 2 days ago

expanded the discussion at equivariant homotopy theory

expanded the statement of the classical Elmendorf theorem

added the statement of the general Elmendorf theorem in general model categories

added remarks on G-equivariant oo-stacks, as special cases of this

- Discussion Type
- discussion topicIoannis Florakis
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicCarlo Angelantonj
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicHandbook of Quantum Gravity
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicT-duality in K-theory classification of topological phases -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

a bare list of references on T-duality in the K-theory classification of topological phases,

to be

`!include`

-ed into the References-subsections of these entries, for ease of synchronization

- Discussion Type
- discussion topicPlücker embedding
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicYuji Kodama
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicKadomtsev-Petviashvili equation
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicmicrolinear space
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Dmitri Pavlov
- Last Active 3 days ago

created microlinear space

One thing I might be mixed up above:

in the literature I have seen it seems to say that

$ X^D x_X X^D \simeq X^{D(2)}$

with

$ D(2) = { (x_1,x_2) \in R \times R | x_i x_j = 0} $.

But shouldn't it be

$ D(2)' = { (x_1,x_2) \in R \times R | x_i^2 = 0} $.

?

- Discussion Type
- discussion topicspin-statistics via configuration spaces -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

this is a bare list of references discussing the spin-statistics theorem for non-relativistic particles via their configuration space of points,

to be

`!include`

-ed into the References-sections of these entries, for ease of synchronization

- Discussion Type
- discussion topicspin-statistics theorem
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active 3 days ago

stub for spin-statistics theorem. Just recording a first few references so far.

- Discussion Type
- discussion topicPCT theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 3 days ago

added missing pointer to

- Raymond F. Streater, Arthur S. Wightman,
*PCT, Spin and Statistics, and All That*, Princeton University Press (1989, 2000) [ISBN:9780691070629, jstor:j.ctt1cx3vcq]

and pointer to:

- Franco Strocchi, §4.3 in:
*An Introduction to Non-Perturbative Foundations of Quantum Field Theory*, Oxford University Press (2013) [doi:10.1093/acprof:oso/9780199671571.001.0001]

- Raymond F. Streater, Arthur S. Wightman,

- Discussion Type
- discussion topicMurray Peshkin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicAndrés F. Reyes-Lega
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicBernd Kuckert
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicBo-Sture Skagerstam
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicGiuseppe Marmo
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicslice theorem
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by DavidRoberts
- Last Active 3 days ago

- Discussion Type
- discussion topicquantum material
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicAlexei B. Sossinsky
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicETCS
- Category Latest Changes
- Started by David_Corfield
- Comments 10
- Last comment by nLab edit announcer
- Last Active 4 days ago

- Discussion Type
- discussion topicboxed knot
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicknot sum
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topic11d SuGra from super C-field flux quantization -- section
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 4 days ago

starting a stand-alone Section-entry (to be

`!include`

ed as a section into*D=11 supergravity*and into*D’Auria-Fré formulation of supergravity*)So far it contains lead-in and statement of the result, in mild but suggestive paraphrase of CDF91, §III.8.5.

I am going to spell out at least parts of the proof, with some attention to the prefactors.

- Discussion Type
- discussion topicMiguel A. Xicoténcatl
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicrelation
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active 5 days ago

- Discussion Type
- discussion topicBPS state
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 5 days ago

I have added to

*BPS state*and to*wall crossing*pointers to two introductory lecture notes

- Discussion Type
- discussion topicManoj K. Prasad
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicconcept with an attitude
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active 5 days ago

This is maybe mainly for entertainment. But don’t forget that for newcomers there is a real issue here which may well be worth explaining:

In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do whith such objects.

Here are examples:

A

*quiver*is just a directed graph (pseudograph, to be explicit). But one says*quiver*instead of*directed graph*when one is interested in studying*quiver representations*: functors from the free category on that graph to the category of finite-dimensional vector spaces.A

*presheaf*is just a contravariant functor. But one says*presheaf*instead of*contravariant functor*when one is interested in studying its sheafification, or even if one is just intersted in regarding the category of functors with its structure of a topos: the presheaf topos.

(…)

- Discussion Type
- discussion topiccounting quantifier
- Category Latest Changes
- Started by Victor Sannier
- Comments 1
- Last comment by Victor Sannier
- Last Active 5 days ago

- Discussion Type
- discussion topicEncyclopedia of Mathematical Physics 2nd ed
- Category Latest Changes
- Started by Urs
- Comments 30
- Last comment by Urs
- Last Active 5 days ago

starting a

`category:reference`

-entry.Just a single item so far, but this entry should incrementally grow as more preprints appear (similar to what we have been doing at

*Handbook of Quantum Gravity*and similar entries).I know that a soft deadline for submissions of at least one of the sections is this December, so I am guessing this is planned to appear in 2024.

- Discussion Type
- discussion topicheterotic string theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active 5 days ago

added pointer to today’s

- Andrea Fontanella, Tomas Ortin,
*On the supersymmetric solutions of the Heterotic Superstring effective action*(arxiv:1910.08496)

- Andrea Fontanella, Tomas Ortin,

- Discussion Type
- discussion topicBayes rule
- Category Latest Changes
- Started by TobyBartels
- Comments 25
- Last comment by David_Corfield
- Last Active 6 days ago

- Discussion Type
- discussion topicChris Kapulkin
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active 6 days ago

- Discussion Type
- discussion topicDaniel Carranza
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Tim_Porter
- Last Active 6 days ago

- Discussion Type
- discussion topicAndy Tonks
- Category Latest Changes
- Started by Tim_Porter
- Comments 4
- Last comment by Tim_Porter
- Last Active 6 days ago

- Discussion Type
- discussion topicgroupoid object in an (infinity,1)-category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by nLab edit announcer
- Last Active 7 days ago

- Discussion Type
- discussion topicHenning Hauschild
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicstochastic dependence and independence
- Category Latest Changes
- Started by PaoloPerrone
- Comments 2
- Last comment by nLab edit announcer
- Last Active 7 days ago