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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 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

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- Discussion Type
- discussion topicring
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by nLab edit announcer
- Last Active Aug 19th 2024

at the beginning of

*ring*I have spelled out a more explicit definition. Also added the examples of rings on cyclic groups to explain the origin of the word “ring”.

- Discussion Type
- discussion topicnonabelian group cohomology
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by Urs
- Last Active Aug 19th 2024

`<div> <p>created <a href="https://ncatlab.org/nlab/show/nonabelian+group+cohomology">nonabelian group cohomology</a></p> <p>the secret title of this entry is "Schreier theory done right". (where "right" is right from the <a href="https://ncatlab.org/nlab/show/nPOV">nPOV</a>)</p> <p>this is the first part of the answer to</p> <blockquote> What is going on at <a href="https://ncatlab.org/nlab/show/nonabelian+Lie+algebra+cohomology">nonabelian Lie algebra cohomology</a>? </blockquote> <p>The second part of the answer is the statement:</p> <blockquote> The same. </blockquote> <p>;-)</p> <p>I'll expand on that eventually.</p> </div>`

- Discussion Type
- discussion topicMackey functor
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by nLab edit announcer
- Last Active Aug 19th 2024

added an Idea-section to

*Mackey functor*(which used to be just a list of references). Also added more references.

- Discussion Type
- discussion topic(infinity,1)-category
- Category Latest Changes
- Started by Urs
- Comments 29
- Last comment by varkor
- Last Active Aug 19th 2024

I worked on brushing up (infinity,1)-category a little

mostly I added in a section on homotopical categories, using some paragraphs from Andre Joyal's message to the CatTheory mailing list.

in this context I also rearranged the order of the subsections

I removed in the introduction the link to the page "Why (oo,1)-categories" and instead expanded the Idea section a bit.

added a paragraph to the beginning of the subsection on model categories

added the new Dugger/Spivak references on the relation between quasi-cats and SSet-cats (added that also to quasi-category and to relation between quasi-categories and simplicial categories)

- Discussion Type
- discussion topicsequential multicategory
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by varkor
- Last Active Aug 19th 2024

- Discussion Type
- discussion topicsoft graviton theorem
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Aug 19th 2024

- Discussion Type
- discussion topicmean-field theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 18th 2024

- Discussion Type
- discussion topicquantum material
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Aug 18th 2024

- Discussion Type
- discussion topicPeter Fulde
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 18th 2024

- Discussion Type
- discussion topiclinguistic semantics
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 18th 2024

Redirects also semantics (linguistics).

- Discussion Type
- discussion topicHorst L. Störmer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 18th 2024

- Discussion Type
- discussion topicidentity type
- Category Latest Changes
- Started by Urs
- Comments 120
- Last comment by nLab edit announcer
- Last Active Aug 18th 2024

added to identity type a mentioning of the alternative definition in terms of inductive types (paths).

- Discussion Type
- discussion topicinter-universal Teichmüller theory
- Category Latest Changes
- Started by Urs
- Comments 150
- Last comment by DavidRoberts
- Last Active Aug 18th 2024

added to

*inter-universal Teichmüller theory*a pointer to the recent note- Yamashita,
*FAQ on ‘Inter-Universality’*(pdf)

(Though after reading I am not sure if that note helps so much.)

- Yamashita,

- Discussion Type
- discussion topicex falso quodlibet
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by J-B Vienney
- Last Active Aug 17th 2024

- Discussion Type
- discussion topicquantum Hall effect via noncommutative geometry -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 17th 2024

a bare list of references, to be

`!include`

-ed into the lists of references of relevant entries (at*quantum hall effect*and*noncommutative geometry*, maybe also at*matrix model*), for ease of synchronizing

- Discussion Type
- discussion topicAlexios P. Polychronakos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2024

- Discussion Type
- discussion topicJainendra K. Jain
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2024

- Discussion Type
- discussion topicSimeon Hellerman
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2024

- Discussion Type
- discussion topicPer Sundell
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 17th 2024

- Discussion Type
- discussion topicanyons in the quantum Hall effect -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Aug 16th 2024

a bare list of references, to be

`!include`

-ed into the References-lists of relevant entries (such as at*anyon*and*quantum Hall effect*) for ease of updating and synchronizing

- Discussion Type
- discussion topicframed link
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by Urs
- Last Active Aug 16th 2024

I tried adding some material to framed link, but as in other recent edits (Dehn twist, Dehn surgery), my efforts might well make an expert smile indulgently. I do mean to – or someone else could – fix up or polish up the recent edit at Dehn surgery, which I’m not particularly happy with at the moment.

- Discussion Type
- discussion topicknot
- Category Latest Changes
- Started by zskoda
- Comments 9
- Last comment by Urs
- Last Active Aug 16th 2024

I added the definition and several references on higher dimensional knots under knot.

- Discussion Type
- discussion topicslice knot
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2024

- Discussion Type
- discussion topicdouble negation
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Aug 16th 2024

I have added to the References at

*double negation*pointer to Andrej’s exposition:which is really good. I have also added this to

*double negation transformation*, but clearly that entry needs some real references, too.

- Discussion Type
- discussion topicYang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Aug 16th 2024

added these two pointers:

Karen Uhlenbeck, notes by Laura Fredrickson,

*Equations of Gauge Theory*, lecture at Temple University, 2012 (pdf)Simon Donaldson,

*Mathematical uses of gauge theory*(pdf)

(if anyone has the date or other data for the second one, let’s add it)

- Discussion Type
- discussion topiccartesian monoidal category
- Category Latest Changes
- Started by David_Corfield
- Comments 9
- Last comment by varkor
- Last Active Aug 16th 2024

Added a link to Todd’s nice page on free cartesian category.

- Discussion Type
- discussion topicAQFT
- Category Latest Changes
- Started by zskoda
- Comments 23
- Last comment by Urs
- Last Active Aug 16th 2024

I did not change anything, I would not like to do it without Urs’s consent and some opinion. The entry AQFT equates algebraic QFT and axiomatic QFT. In the traditional circle, algebraic quantum field theory meant being based on local nets – local approach of Haag and Araki. This is what the entry now describes. The Weightman axioms are somewhat different, they are based on fields belonging some spaces of distributions, and 30 years ago it was called field axiomatics, unlike the algebraic axiomatics. But these differences are not that important for the main entry on AQFT. What is a bigger drawback is that the third approach to axiomatic QFT if very different and was very strong few decades ago and still has some followers. That is the

**S-matrix axiomatics**which does not believe in physical existence of observables at finite distance, but only in the asymptotic values given by the S-matrix. The first such axiomatics was due Bogoliubov, I think. (Of course he later worked on other approaches, especially on Wightman’s. Both the Wightman’s and Bogoliubov’s formalisms are earlier than the algebraic QFT.)I would like to say that axiomatic QFT has 3 groups of approaches, and especially to distinguish S-matrix axiomatics from the “algebraic QFT”. Is this disputable ?

- Discussion Type
- discussion topicSidney D. Drell
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 16th 2024

- Discussion Type
- discussion topicperturbative quantum field theory
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Aug 16th 2024

I have further expanded the Idea-section and the list of commented references at

*perturbative quantum field theory*.(Not proof-read yet, need to run to catch a train.)

- Discussion Type
- discussion topicdual number
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 15th 2024

- Discussion Type
- discussion topiccompact closed category
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 15
- Last comment by John Baez
- Last Active Aug 15th 2024

I added a note to compact closed category on the fact that the inclusion from compact closed categories into SMCCs has a left adjoint, pointing to an article by Day where he describes the free compact closed category over a closed symmetric monoidal category as a localization. Question: this left adjoint is not full, but I believe it is faithful – does anyone know how to prove that?

- Discussion Type
- discussion topicSeverin Bunk
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by nLab edit announcer
- Last Active Aug 15th 2024

- Discussion Type
- discussion topicdualizable object
- Category Latest Changes
- Started by Urs
- Comments 35
- Last comment by John Baez
- Last Active Aug 15th 2024

edited dualizable object a little, added a brief paragraph on dualizable objects in symmetric monoidal $(\infty,n)$-categories

- Discussion Type
- discussion topicgroup object
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by John Baez
- Last Active Aug 14th 2024

Added to group object the Yoneda-embedding-style definition and added supergroup to the list of examples.

- Discussion Type
- discussion topicextension (double category theory)
- Category Latest Changes
- Started by mattecapu
- Comments 1
- Last comment by mattecapu
- Last Active Aug 14th 2024

- Discussion Type
- discussion topicrestriction (double category theory)
- Category Latest Changes
- Started by mattecapu
- Comments 1
- Last comment by mattecapu
- Last Active Aug 14th 2024

- Discussion Type
- discussion topictight and loose morphisms
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by mattecapu
- Last Active Aug 14th 2024

- Discussion Type
- discussion topiccompanion pair
- Category Latest Changes
- Started by mattecapu
- Comments 7
- Last comment by mattecapu
- Last Active Aug 14th 2024

- Discussion Type
- discussion topicconjunction
- Category Latest Changes
- Started by mattecapu
- Comments 2
- Last comment by mattecapu
- Last Active Aug 14th 2024

same as in companion pair

- Discussion Type
- discussion topicdescent morphism
- Category Latest Changes
- Started by Mike Shulman
- Comments 33
- Last comment by DavidRoberts
- Last Active Aug 14th 2024

Created descent morphism.

In adding links, I discovered that Euclidean-topological infinity-groupoid and separated (infinity,1)-presheaf use the phrase “descent morphism” to refer to the

*comparison functor*mapping into the category of descent data. If no one has any objections, I would like to change this to avoid confusion, but I’m not sure what to change it to: would “comparison functor” be good enough?

- Discussion Type
- discussion topicManuela Sobral
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Aug 14th 2024

- Discussion Type
- discussion topicsemantics
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Aug 10th 2024

- Discussion Type
- discussion topicmodel
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 10th 2024

I felt we needed a dedicated entry on model/category of models. So I started one. But just a puny stub so far.

- Discussion Type
- discussion topicisomorphism in a Segal type
- Category Latest Changes
- Started by Guest
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topiccohesive homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 38
- Last comment by nLab edit announcer
- Last Active Aug 9th 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 topicRezk type
- Category Latest Changes
- Started by Guest
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topicbounded total order
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topicop modality
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topichom type
- Category Latest Changes
- Started by Guest
- Comments 2
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topicparametric dependent type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

starting page on type theories with parametricity, as a separate article from the article on polymorphism.

Anonymouse

- Discussion Type
- discussion topicUlrik Buchholtz
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

Adding reference

- Ulrik Buchholtz,
*Higher Structures in Homotopy Type Theory*, in:*Reflections on the Foundations of Mathematics*, Synthese Library**407**Springer (2019) [doi:10.1007/978-3-030-15655-8_7, arXiv:1807.02177]

Anonymouse

- Ulrik Buchholtz,

- Discussion Type
- discussion topicJonathan Weinberger
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topicDaniel Gratzer
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topicdirected univalence axiom
- Category Latest Changes
- Started by Guest
- Comments 2
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topicsimplicial type theory
- Category Latest Changes
- Started by nLab edit announcer
- Comments 5
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topiccoCartesian fibration of (∞,1)-operads
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

- Discussion Type
- discussion topicspin-statistics theorem
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by Urs
- Last Active Aug 9th 2024

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

- Discussion Type
- discussion topicGiry monad
- Category Latest Changes
- Started by zskoda
- Comments 74
- Last comment by nLab edit announcer
- Last Active Aug 9th 2024

Added a reference of Robert Furber, Bart Jacobs at Giry monad.

- Discussion Type
- discussion topicexponentiable functor
- Category Latest Changes
- Started by John Baez
- Comments 12
- Last comment by SiyaM
- Last Active Aug 9th 2024

I added the word “strict” here:

The theorem is then that the following are equivalent:

- $p$ is a
**strict**Conduché functor. - $p$ is exponentiable in the 1-category $Cat$.
- $p$ is exponentiable in the strict 2-category $Cat$.

because strict and weak Conduché functors are being distinguished in this article.

- $p$ is a

- Discussion Type
- discussion topic2-category
- Category Latest Changes
- Started by Urs
- Comments 34
- Last comment by varkor
- Last Active Aug 8th 2024

promted by demand from my Basic-Course-On-Category-Theory-Students I expanded the entry 2-category:

mentioned more relations to other concepts in the Idea-section;

added an Examples-section with a bunch of (classes of) examples;

added a list of references. Please add more if you can think of more!