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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 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 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 subobject 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 topicDonaldson theory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jun 26th 2024

added to

*Donaldson theory*a pointer back to*Lagrangian correspondences and category-valued TFT*

- Discussion Type
- discussion topicDrinfeld associator
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by nLab edit announcer
- Last Active Jun 26th 2024

Added

- V. G. Drinfeld,
*Quasi-Hopf algebras and Knizhnik-Zanolodchikov equations*, Acad. Sci. Ukrainian SSR, Institute for Theoretical Physics, Preprint ITP-89-43B (Kiev 1989) pdf

P.S. erased later, the reference is not directly appropriate for this entry.

- V. G. Drinfeld,

- Discussion Type
- discussion topicBargmann-Fock space
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Jun 26th 2024

- Discussion Type
- discussion topiccohesive homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by nLab edit announcer
- Last Active Jun 26th 2024

I am working on an entry cohesive homotopy type theory.

This started out as material split off from cohesive (infinity,1)-topos, but is expanding now.

- Discussion Type
- discussion topicTomasz Mrowka
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 26th 2024

Created new article with papers introducing the Kronheimer-Mrowka basic classes.

- Discussion Type
- discussion topicKronheimer-Mrowka basic class
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 26th 2024

Created new article for Kronheimer-Mrowka basic classes. (The german Wikipedia entry is now also available.)

- Discussion Type
- discussion topicSimon Donaldson
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 26th 2024

Added writings, in which he proved Donaldson’s theorem.

- Discussion Type
- discussion topicintersection pairing
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Samuel Adrian Antz
- Last Active Jun 26th 2024

stub for

*intersection pairing*

- Discussion Type
- discussion topicDonaldson's theorem
- Category Latest Changes
- Started by Samuel Adrian Antz
- Comments 1
- Last comment by Samuel Adrian Antz
- Last Active Jun 26th 2024

Created new article for Donaldson’s theorem. (The german Wikipedia entry is now also available.)

- Discussion Type
- discussion topicautomorphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 26th 2024

added pointer to:

- Marshall Hall, §6 in:
*The Theory of Groups*, Macmillan (1959), AMS Chelsea (1976), Dover (2018) [ISBN:978-0-8218-1967-8, ISBN:9780486816906]

- Marshall Hall, §6 in:

- Discussion Type
- discussion topicholomorph
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Jun 26th 2024

- Discussion Type
- discussion topicMarshall Hall
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 26th 2024

- Discussion Type
- discussion topicgroup theory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Jun 26th 2024

added pointer to:

Eugene P. Wigner

*Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren*, Springer (1931) [doi:10.1007/978-3-663-02555-9, pdf]Eugene P. Wigner,

*Group theory: And its application to the quantum mechanics of atomic spectra*, 5, Academic Press (1959) [doi:978-0-12-750550-3]

- Discussion Type
- discussion topicJordan curve theorem
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by nLab edit announcer
- Last Active Jun 26th 2024

In the process of beginning to compile a list of central theorems in topology, on top of the list of basic facts in topology that I had been compiling the last days (of course there is some remaining ambiguity in which of these two lists to place a given item) I have created a stub for

*Jordan curve theorem*.

- Discussion Type
- discussion topicDaniel Bump
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by DavidRoberts
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicMaurer-Cartan form
- Category Latest Changes
- Started by Urs
- Comments 34
- Last comment by Urs
- Last Active Jun 25th 2024

wrote Maurer-Cartan form

the first part is the standard story, but I chose a presentation which I find more insightful than the standard symbol chains as on Wikipedia.

then there is a section on Maurer-Cartan forms on oo-Lie groups and how that reduces to the standard story for ordinary Lie groups.

The detailed statements and proofs of this second part are at Lie infinity-groupoid in the new section The canonical form on a Lie oo-group that is just a Lie group.

- Discussion Type
- discussion topicBargmann-Segal transform
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Urs
- Last Active Jun 25th 2024

- Discussion Type
- discussion topiccoherent state
- Category Latest Changes
- Started by zskoda
- Comments 6
- Last comment by zskoda
- Last Active Jun 25th 2024

I changed back the name of the page to coherent state. Though it is usually considered in quantum mechanics, and the name is still correct, as a specialist in the area of coherent states, I have almost never seen the phrase “coherent quantum state” written out in mathematical physics, so I would prefer to have this long unusual name as a redirect only. Of course, we often talk about the coherence of quantum states. But this is about a general feature of coherence, like in optics. The specific states in mathematical physics which, among other features, have such coherence properties are usually called squeezed coherent states, and the coherent states of these entry are even more specific than those. I am about to add a couple of new references, so I came across the page again.

- Discussion Type
- discussion topicquantum symmetric pair
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicIwasawa decomposition
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by zskoda
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicTits system
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicLie group
- Category Latest Changes
- Started by Urs
- Comments 15
- Last comment by Urs
- Last Active Jun 25th 2024

tried to bring the entry Lie group a bit into shape: added plenty of sections and cross links to other nLab material. But there is still much that deserves to be done.

- Discussion Type
- discussion topicArtin-Schelter regular algebra
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by Urs
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicGeorgia Benkart
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicGerstenhaber algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jun 25th 2024

created stub for Gerstenhaber algebra

- Discussion Type
- discussion topicBruhat decomposition
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by zskoda
- Last Active Jun 25th 2024

started

*Bruhat decomposition*, so far just the plain definitionthe same paragraph I also included at

*Schubert calculus*

- Discussion Type
- discussion topicAnthony Joseph
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicGail Letzter
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicregular local ring
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Jun 25th 2024

Expanding slightly this entry and also Cohen-Macauley ring.

- Discussion Type
- discussion topicheap
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 22
- Last comment by John Baez
- Last Active Jun 25th 2024

- Discussion Type
- discussion topicindexing system
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by Urs
- Last Active Jun 24th 2024

- Discussion Type
- discussion topicmicroscopic AdS-CFT via p-brane sigma-models -- references
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jun 24th 2024

a bare list of references, to be

`!include`

-ed into the References-section of relevant entries (such as*AdS/CFT correspondence*,*super p-brane sigma moel*,*black brane*and*superconformal multiplet*) for ease of synchronization.(These are mostly references that I had long kept at the first two of these entries. But now that I added a couple more, it’s good time to clean this up with a single

`!include`

-entry.)

- Discussion Type
- discussion topicgeometrodynamics
- Category Latest Changes
- Started by Eric
- Comments 9
- Last comment by Urs
- Last Active Jun 24th 2024

Created a stub with some references for geometrodynamics.

- Discussion Type
- discussion topicblack brane
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jun 24th 2024

stub for black brane

- Discussion Type
- discussion topicmatching KN-black holes to elementary particles -- references
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 24th 2024

a bare list of references, to be

`!include`

-ed into the References-section of relevant entries (such as at*black brane*and*Kerr-Newman black hole*), for ease of synchronizing

- Discussion Type
- discussion topicKerr-Newman spacetime
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 24th 2024

added pointer to:

- Tim Adamo, E. T. Newman,
*The Kerr-Newman metric: A Review*, Scholarpedia 9: 31791 (2014) [arXiv:1410.6626, doi:10.4249/scholarpedia.31791, pdf]

- Tim Adamo, E. T. Newman,

- Discussion Type
- discussion topicHeine-Cantor theorem
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Jun 24th 2024

- Discussion Type
- discussion topicsigma-topological space
- Category Latest Changes
- Started by Guest
- Comments 3
- Last comment by Urs
- Last Active Jun 24th 2024

- Discussion Type
- discussion topicprelattice-ordered commutative monoid
- Category Latest Changes
- Started by J-B Vienney
- Comments 2
- Last comment by Urs
- Last Active Jun 24th 2024

- Discussion Type
- discussion topicMac Lane's proof of the coherence theorem for monoidal categories
- Category Latest Changes
- Started by ltrujello
- Comments 5
- Last comment by J-B Vienney
- Last Active Jun 24th 2024

I’m interested in editing

*Mac Lane’s proof of the coherence theorem for monoidal categories*, as I recently went through all the gory details myself and wrote it up. I was wondering if anybody has any thoughts on what should be left alone with regard to any future changes. Many people clearly put in a lot of work into the page, but it looks like people got busy and it hasn’t been updated in a while.I think the first few paragraphs are fine, but I think the rest is a bit wordy, it could be more formal, and notation could be changed (very slightly) to be less clunky. I specifically want to make the current document more formal (e.g., saying “Definition: blah blah”), include some nice diagrams, change the notation (e.g., to avoid using double primes, to avoid denoting a monoidal category as B since I think the letter M pedagogically makes more sense), and complete the incomplete entries at the bottom. I’m not really sure if anyone would be against such changes, hence my inquiry.

- Discussion Type
- discussion topictraced monoidal category
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by J-B Vienney
- Last Active Jun 23rd 2024

created

*traced monoidal category*with a bare minimumI would have sworn that we already had an entry on that, but it seems we didn’t. If I somehow missed it , let me know and we need to fix things then.

- Discussion Type
- discussion topicfunction
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jun 23rd 2024

promted by the creation of

*quadratic function*I have added, under “Related concepts”:

- Discussion Type
- discussion topicpp-wave spacetime
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jun 23rd 2024

- Discussion Type
- discussion topicGCD ring
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by J-B Vienney
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicGCD domain
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by J-B Vienney
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicA1-homotopy type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicaxiom of cohesion
- Category Latest Changes
- Started by nLab edit announcer
- Comments 11
- Last comment by nLab edit announcer
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicPiet Claus
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicspin chain
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicfractured homotopy type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicBMN matrix model
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicGabriel–Ulmer duality
- Category Latest Changes
- Started by nLab edit announcer
- Comments 13
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicSimon Philip
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicFederica Pasqualone
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topiccomplete intersection ring
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicstraightening functor
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 13
- Last comment by nLab edit announcer
- Last Active Jun 22nd 2024

Added:

## Related concepts

## References

The original result is due to Lurie:

A considerably simplified presentation is available in

- Fabian Hebestreit, Gijs Heuts, Jaco Ruit,
*A short proof of the straightening theorem*, arXiv:2111.00069.

- Fabian Hebestreit, Gijs Heuts, Jaco Ruit,

- Discussion Type
- discussion topicvon Neumann regular ring
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicCapelli identity
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Jun 22nd 2024

- Discussion Type
- discussion topicmonadicity theorem
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by nLab edit announcer
- Last Active Jun 22nd 2024

at monadicity theorem in the second formulation of the theorem, item 3, it said

$C$ has

I think it must be

$D$ has

and have changed it accordingly. But have a look.

- Discussion Type
- discussion topicgroup algebra
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by J-B Vienney
- Last Active Jun 21st 2024

the entry

*group algebra*had been full of notation mismatch and also of typos. I have reworked it now.