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 finite 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 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

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 topicface algebra
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 6 minutes ago

- Discussion Type
- discussion topicThe Stacks Project
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by RodMcGuire
- Last Active 1 hour ago

created a “category: reference”-page The Stacks Project

I have only now had a closer look at this and am impressed by the scope this has. Currently a total of 2288 pages. It starts with all the basics, category theory, commutative algebra and works its way through all the details to arrive at algebraic stacks.

So besides my usual complaint (Why behave as if there are not sites besides the usual suspects on $CRing^{op}$ and either give a general account or call this

*The Algebraic Stacks Project*? ) I am enjoying seeing this. We should have lots of occasion to link to this. Too bad that this did not start out as a wiki.

- Discussion Type
- discussion topicplethory
- Category Latest Changes
- Started by Joe Moeller
- Comments 6
- Last comment by varkor
- Last Active 1 hour ago

- Discussion Type
- discussion topicTall-Wraith monoid
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by varkor
- Last Active 2 hours ago

- Discussion Type
- discussion topicbimodel
- Category Latest Changes
- Started by varkor
- Comments 2
- Last comment by varkor
- Last Active 2 hours ago

- Discussion Type
- discussion topicYifei Zhao
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 9 hours ago

- Discussion Type
- discussion topiccoalgebroid
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active 10 hours ago

- Discussion Type
- discussion topicinfinitary algebraic theory
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by varkor
- Last Active 13 hours ago

Added this reference

- Martin Brandenburg,
*Large limit sketches and topological space objects*(arXiv:2106.11115)

- Martin Brandenburg,

- Discussion Type
- discussion topictype II geometry
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 15 hours ago

stub for

*type II geometry*

- Discussion Type
- discussion topicquantum measurement
- Category Latest Changes
- Started by Urs
- Comments 25
- Last comment by Urs
- Last Active 16 hours ago

created a currently fairly empty entry

*quantum measurement*, just so as to have a place where to give a commented pointer to the article- Klaas Landsman, Robin Reuvers,
*A Flea on Schrödinger’s Cat*, Found. Phys. 43, 373-407 (2013) (arXiv:1210.2353)

- Klaas Landsman, Robin Reuvers,

- Discussion Type
- discussion topicduality in string theory
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active 2 days ago

I needed an entry to be able to point to which collects pointers to the various entries on “dualities” in string theory. So I created one:

*duality in string theory*.

- Discussion Type
- discussion topicTr(ϕ³)
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

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

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

- Discussion Type
- discussion topicquantum symmetric pair
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by zskoda
- Last Active 3 days ago

- Discussion Type
- discussion topicFox derivative
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topiclift
- Category Latest Changes
- Started by David_Corfield
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicTychonoff theorem
- Category Latest Changes
- Started by Urs
- Comments 33
- Last comment by nLab edit announcer
- Last Active 3 days ago

I have edited at

*Tychonoff theorem*:tidied up the Idea-section. (Previously there was a long paragraph on the spelling of the theorem before the content of the theorem was even mentioned)

moved the proofs into a subsection “Proofs”, and added a pointer to an elementary proof of the finitary version, here

Notice that there is an ancient query box in the entry, with discussion between Todd and Toby. It would be good to remove this box and turn whatever conclusion was reached into a proper part of the entry.

At then end of the entry there is a line:

More details to appear at Tychonoff theorem for locales

which however has not “appeared” yet.

But since the page is not called “Tychonoff theorem for topological spaces”, and since it already talks about locales a fair bit in the Idea section, I suggest to remove that line and to simply add all discussion of localic Tychonoff to this same entry.

- Discussion Type
- discussion topiclifting property
- Category Latest Changes
- Started by David_Corfield
- Comments 29
- Last comment by David_Corfield
- Last Active 3 days ago

Started lift.

weak factorization system has redirects from: lifting property, right lifting property, left lifting property, lifting problem, lifting problems.

Would it be better to have these redirect to lift?

- Discussion Type
- discussion topicsuper-moduli of super Riemann surfaces -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 3 days ago

a bare subsection with a list of references, to be

`!include`

-ed at*super Riemann surface*and at*moduli space of super Riemann surfaces*, for ease of synchronization

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

added pointer to today’s

- Yuta Nozaki, Yuya Koda, Muneto Nitta:
*Quantum Knots that Never Come Untied Michikazu Kobayashi*[arXiv:2410.07470]

- Yuta Nozaki, Yuya Koda, Muneto Nitta:

- Discussion Type
- discussion topick-morphism
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active 4 days ago

For the purposes of negative thinking, it may be useful to recognise that every $\infty$-category has a $(-1)$-morphism, which is the source and target of every object. (In the geometric picture, this comes as the $(-1)$-simplex of an augmented simplicial set.)

Jonathan Arnoult has pointed out on CT Zulip that this is misleading: it sounds like it implies that every $\infty$-category is monoidal! And John Baez pointed out that the analogy to augmented simplicial sets fails because in an augmented simplicial set each 0-simplex has only

*one*face, rather than a separate “source” and “target” that are both the same $(-1)$-simplex.I suggest we just remove this paragraph and the query box following it, since I can’t think of a way to rephrase it that would be more helpful than unhelpful. But I’m open to other suggestions.

- Discussion Type
- discussion topicfibrant double category
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by varkor
- Last Active 4 days ago

created quick stub for framed bicategory

but my machine's battery will die any second now...

- Discussion Type
- discussion topicstring theory
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active 4 days ago

I have added to string theory a new section Critical strings and quantum anomalies.

Really I was beginning to work on a new entry twisted spin^c structure (not done yet) and then I found that a summary discussion along the above lines had been missing.

- Discussion Type
- discussion topicprinciple of extremal action
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active 4 days ago

for discussion at

*geometry of physics*I needed to be able to point to*principle of extremal action*, so I created a little entry.

- Discussion Type
- discussion topicKimmo Rosenthal
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active 4 days ago

I added a reference on Gabriel filters on quantales.

Very strange: version one on show had a reference on Etendues (entered by T. Holder), but when I clicked edit there was none in the edit window, just in show window. I edited and one can not see it in any history, nowhere. So there was something in show cache from 2014 which is not recorded in any history edit.

- Discussion Type
- discussion topicfr-code
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 4 days ago

starting something on the concept introduced in

Sergei O. Ivanov, Roman Mikhailov:

*A higher limit approach to homology theories*, Journal of Pure and Applied Algebra**219**6 (2015) 1915-1939 [arXiv:1309.4920, doi:10.1016/j.jpaa.2014.07.016]Sergei O. Ivanov, Roman Mikhailov:

*Higher limits, homology theories and $\mathbf{fr}$-codes*, in:*Combinatorial and Toric Homotopy*, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (2017) 229-261 [arXiv:1510.09044, doi:10.1142/9789813226579_0004]

but for the moment there is little more than these references

- Discussion Type
- discussion topic2-Hilbert space
- Category Latest Changes
- Started by John Baez
- Comments 1
- Last comment by John Baez
- Last Active 5 days ago

- Discussion Type
- discussion topicstrictification for bicategories with finite limits
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by varkor
- Last Active 5 days ago

- Discussion Type
- discussion topicsurfaceology
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 5 days ago

- Discussion Type
- discussion topicdinatural transformation
- Category Latest Changes
- Started by Mike Shulman
- Comments 8
- Last comment by nLab edit announcer
- Last Active 5 days ago

Expanded dinatural transformation a little with examples and references.

- Discussion Type
- discussion topicelementary function arithmetic
- Category Latest Changes
- Started by Victor Sannier
- Comments 1
- Last comment by Victor Sannier
- Last Active 5 days ago

- Discussion Type
- discussion topicFourier-Mukai transform
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 5 days ago

I gave

*Fourier-Mukai transform*a bit of an Idea-section. It overlaps substantially with the Definition section now, but I thought one needs to say the simple basic idea clearly in words first. Also added a few more pointers to literature.

- Discussion Type
- discussion topicmatrix
- Category Latest Changes
- Started by RodMcGuire
- Comments 7
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicgeometrical formulation of quantum mechanics
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicAdams operation
- Category Latest Changes
- Started by John Baez
- Comments 8
- Last comment by John Baez
- Last Active 5 days ago

I added a clearer “The idea” section for Adams operation, and changed the word “functorial” to “natural” in a number of places, because while various sources do say the Adams operations are functorial, they must really be natural transformations from the functor $K: Top \to AbGp$ to itself.

- Discussion Type
- discussion topicBerezin quantization
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicring of Witt vectors
- Category Latest Changes
- Started by John Baez
- Comments 7
- Last comment by John Baez
- Last Active 5 days ago

- Discussion Type
- discussion topicModern foundations for stable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Anisomorphism
- Last Active 5 days ago

I am giving

*Modern foundations for stable homotopy theory*a category:reference entry.First thing I did was to brush-up the list of references at

*symmetric smash product of spectra*. Then I copied over the nicely to-the-point History-paragraph to a new section*stable homotopy theory – history*.

- Discussion Type
- discussion topicTor
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Anisomorphism
- Last Active 5 days ago

have now spelled out at

*Tor*in simple terms how $Tor_1^{Ab}(A,B)$ is a torsion group, so far for the case that $A$ is finite.

- Discussion Type
- discussion topicequalizer
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by maxsnew
- Last Active 6 days ago

added to equalizer statement and proof that a category has equalizers if it has pullbcks and products

- Discussion Type
- discussion topicreal oriented cohomology theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 6 days ago

- Discussion Type
- discussion topicPaul Wilson
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topiccoherence and strictification for symmetric monoidal categories
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topicSven Krippendorf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

- Discussion Type
- discussion topicentropy
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by kensmosis
- Last Active 6 days ago

I have added

- Paolo Facchi, Giovanni Gramegna, Arturo Konderak,
*Entropy of quantum states*(arXiv:2104.12611)

and added publication details to

- A. P. Balachandran, T. R. Govindarajan, Amilcar R. de Queiroz, A. F. Reyes-Lega,
*Algebraic approach to entanglement and entropy*, Phys. Rev. A 88, 022301 (2013) (arXiv:1301.1300)

and grouped together more discernibly the references on operator-algebraic entropy

- Paolo Facchi, Giovanni Gramegna, Arturo Konderak,

- Discussion Type
- discussion topiccore groupoid
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by John Baez
- Last Active 7 days ago

added at

*core*the remark that the core is right adjoint to the forgetful functor $Grpd \to Cat$.

- Discussion Type
- discussion topicsynthetic mathematics
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Victor Sannier
- Last Active 7 days ago

felt the desire to have an entry on the general idea (if any) of

*synthetic mathematics*, cross-linking with the relevant examples-entries.This has much room for being further expanded, of course.

- Discussion Type
- discussion topicquasi-Hopf algebra
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by perezl.alonso
- Last Active 7 days ago

The Idea-section at

*quasi-Hopf algebra*had been confused and wrong. I have removed it and written a new one.

- Discussion Type
- discussion topicBFSS matrix model
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicsmooth homotopy
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 7 days ago

- Discussion Type
- discussion topicJohn Rognes
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Oct 6th 2024

- Discussion Type
- discussion topicPeter Freyd
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by varkor
- Last Active Oct 6th 2024

Adding reference

- Peter Freyd,
*Algebraic real analysis*, Theory and Applications of Categories, Vol. 20, 2008, No. 10, pp 215-306 (tac:20-10)

Anonymous

- Peter Freyd,

- Discussion Type
- discussion topicintrospective theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Oct 5th 2024

- Discussion Type
- discussion topicSegal type
- Category Latest Changes
- Started by Guest
- Comments 7
- Last comment by jonsterling
- Last Active Oct 5th 2024

- Discussion Type
- discussion topicEncyclopedia of Mathematical Physics 2nd ed
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by Urs
- Last Active Oct 5th 2024

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 topicWigner classification
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 5th 2024

Have added pointer to:

- Adam Caulton:
*Is a particle an irreducible representation of the Poincaré group?*[arXiv:2410.02354]

(but I haven’t more than skimmed it and don’t mean to endorse it).

- Adam Caulton:

- Discussion Type
- discussion topicgeometric realization of categories
- Category Latest Changes
- Started by nLab edit announcer
- Comments 12
- Last comment by Urs
- Last Active Oct 5th 2024

- Discussion Type
- discussion topicBarratt nerve
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 5th 2024

- Discussion Type
- discussion topicWilliam Goldman
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Oct 5th 2024