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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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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 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 topicaffine logic
- Category Latest Changes
- Started by David_Corfield
- Comments 16
- Last comment by nLab edit announcer
- Last Active Sep 6th 2024

I started a stub at affine logic as I saw the link requested in a couple of places.

- Discussion Type
- discussion topiclinear logic
- Category Latest Changes
- Started by Mike Shulman
- Comments 43
- Last comment by nLab edit announcer
- Last Active Sep 6th 2024

The cut rule for linear logic used to be stated as

If $\Gamma \vdash A$ and $A \vdash \Delta$, then $\Gamma \vdash \Delta$.

I don’t think this is general enough, so I corrected it to

If $\Gamma \vdash A, \Phi$ and $\Psi,A \vdash \Delta$, then $\Psi,\Gamma \vdash \Delta,\Phi$.

- Discussion Type
- discussion topicunified topological space
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Sep 6th 2024

- Discussion Type
- discussion topicGalois theory
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by David_Corfield
- Last Active Sep 6th 2024

the entry Galois theory used to be a stub with only some links. I have now added plenty of details.

- Discussion Type
- discussion topicAlexander Grothendieck
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Sep 6th 2024

I have tried to expand a bit the text at the beginning of the category:people entry

*Alexander Grothendieck*, mention more of what his work was about, add more hyperlinks. It could still be much improved, but right now it reads as follows:The french mathematician

**Alexandre Grothendieck**, (in English usually Alexander Grothendieck), has created a work whose influence has shown him to be the greatest pure mathematician of the 20th century; and his ideas continue to be developed in this century.Initially working on topological vector spaces and analysis, Grothendieck then made revolutionary advances in algebraic geometry by developing sheaf and topos theory and abelian sheaf cohomology and formulating algebraic geometry in these terms (locally ringed spaces, schemes). Later topos theory further developed independently and today serves as the foundation also for other kinds of geometry. Notably its homotopy theoretic refinement to higher topos theory serves as the foundation for modern derived algebraic geometry.

Grothendieck’s work is documented in texts known as EGA (with Dieudonné), an early account FGA, and the many volume account SGA of the seminars at l’IHÉS, Bures-sur-Yvette, where he was based at the time. (See the wikipedia article for some indication of the story from there until the early 1980s.)

By the way, in view of the recent objection to referring to people as “famous” in category:people entries: the lead-in sentence here is not due to me, it has been this way all along. One might feel that it should be rephrased, but I leave that to those who feel strongly about it.

- Discussion Type
- discussion topicquantum field theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Sep 6th 2024

wrote an Idea-section at quantum field theory

- Discussion Type
- discussion topicN-∞ operad
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by Urs
- Last Active Sep 5th 2024

- Discussion Type
- discussion topicseparable monad
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Sep 5th 2024

- Discussion Type
- discussion topicHeyting field
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by nLab edit announcer
- Last Active Sep 5th 2024

- Discussion Type
- discussion topicRel
- Category Latest Changes
- Started by John Baez
- Comments 6
- Last comment by mattecapu
- Last Active Sep 5th 2024

- Discussion Type
- discussion topicrepresentable 2-category
- Category Latest Changes
- Started by varkor
- Comments 7
- Last comment by AlexanderCampbell
- Last Active Sep 4th 2024

- Discussion Type
- discussion topicdifferential crossed module
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 4th 2024

added pointer to:

- Johannes Huebschmann,
*On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras*[arXiv:2208.02539]

- Johannes Huebschmann,

- Discussion Type
- discussion topicindex
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 4th 2024

I gave

*index*an Idea-section.In the course of this I created some stubby auxiliary entries, such as (in rapidly increasing order of stubbieness)

- Discussion Type
- discussion topicDaniel V. Tausk
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2024

- Discussion Type
- discussion topicAlessandro Portaluri
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 4th 2024

- Discussion Type
- discussion topicMaslov index
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 4th 2024

Added to

*Maslov index*and to*Lagrangian Grassmannian*the following quick cohomological definition of the Maslov index:

The first ordinary cohomology of the stable Lagrangian Grassmannian with integer coefficients is isomorphic to the integers

$H^1(LGrass, \mathbb{Z}) \simeq \mathbb{Z} \,.$The generator of this cohomology group is called the

$u \in H^1(LGrass, \mathbb{Z}) \,.$*universal Maslov index*Given a Lagrangian submanifold $Y \hookrightarrow X$ of a symplectic manifold $(X,\omega)$, its tangent bundle is classified by a function

$i \;\colon\; Y \to LGrass \,.$The _Maslov index of $Y$ is the universal Maslov index pulled back along this map

$i^\ast u \in H^1(Y,\mathbb{Z}) \,.$

- Discussion Type
- discussion topicreduction modulo prime
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Sep 4th 2024

- Discussion Type
- discussion topicLouis Halle Rowen
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Sep 3rd 2024

- Discussion Type
- discussion topicAlexei Kanel Belov
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by zskoda
- Last Active Sep 3rd 2024

- Discussion Type
- discussion topicBergman's centralizer theorem
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Sep 3rd 2024

- Discussion Type
- discussion topicnilpotent Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by zskoda
- Last Active Sep 3rd 2024

- Discussion Type
- discussion topicBurnside ring
- Category Latest Changes
- Started by Todd_Trimble
- Comments 55
- Last comment by nLab edit announcer
- Last Active Sep 3rd 2024

I added a Definition section to Burnside ring (and made Burnside rig redirect to it).

- Discussion Type
- discussion topicChetan Vuppulury
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicNivedita
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicCameron Krulewski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicBrett Hungar
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicGiovanni Ferrer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicdagger category
- Category Latest Changes
- Started by Urs
- Comments 43
- Last comment by nLab edit announcer
- Last Active Sep 2nd 2024

I took the liberty of incorporating material from Andre Joyal's latest message to the CatTheory mailing list into the entry dagger-category:

created sections

- Discussion Type
- discussion topicWedderburn-Artin theorem
- Category Latest Changes
- Started by John Baez
- Comments 6
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicJoseph Wedderburn
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicCauchy structure
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by nLab edit announcer
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicJean-Pierre Serre
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicEugene B. Dynkin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicindexing system
- Category Latest Changes
- Started by nLab edit announcer
- Comments 7
- Last comment by nLab edit announcer
- Last Active Sep 2nd 2024

- Discussion Type
- discussion topicKreisel-Lacombe-Shoenfield-Tseitin theorem
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active Sep 1st 2024

- Discussion Type
- discussion topicDrinfeld center
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by perezl.alonso
- Last Active Sep 1st 2024

- Discussion Type
- discussion topicLie algebra
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Sep 1st 2024

added to

*Lie algebra*a brief paragraph*general abstract perspective*to go along with this MO reply

- Discussion Type
- discussion topicstring diagram
- Category Latest Changes
- Started by nLab edit announcer
- Comments 51
- Last comment by Urs
- Last Active Sep 1st 2024

- Discussion Type
- discussion topicYuli Rudyak
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 1st 2024

- Discussion Type
- discussion topicTractatus Logico-Philosophicus
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Sep 1st 2024

- Discussion Type
- discussion topicShum's theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 1st 2024

- Discussion Type
- discussion topicpartial order
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by zskoda
- Last Active Aug 31st 2024

added statement of existence of linear extensions (here)

Will give this its own entry at

*linear extension of a partial order*, for ease of referencing

- Discussion Type
- discussion topicphilosophy - contents
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Aug 31st 2024

[spam]

- Discussion Type
- discussion topictangle
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 5
- Last comment by Urs
- Last Active Aug 31st 2024

- Discussion Type
- discussion topicLudwig Wittgenstein
- Category Latest Changes
- Started by J-B Vienney
- Comments 2
- Last comment by Urs
- Last Active Aug 31st 2024

- Discussion Type
- discussion topicribbon category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 9
- Last comment by Urs
- Last Active Aug 31st 2024

- Discussion Type
- discussion topicW algebra
- Category Latest Changes
- Started by zskoda
- Comments 2
- Last comment by perezl.alonso
- Last Active Aug 31st 2024

An early survey is

- Peter Bouwknegt, Kareljan Schoutens,
*W symmetry in conformal field theory*, Phys. Rep.**223**:4 (1993) 183–276 doi

- Peter Bouwknegt, Kareljan Schoutens,

- Discussion Type
- discussion topicsupergeometry
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Aug 30th 2024

added to supergeometry a link to the recent talk

- Mikhail Kapranov,
*Categorification of supersymmetry and stable homotopy groups of spheres*(video)

- Mikhail Kapranov,

- Discussion Type
- discussion topicsupergroup
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Aug 30th 2024

Added the Yoneda-embedding way to talk about group objects and hence supergroups.

- Discussion Type
- discussion topicJoscha Diehl
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Aug 30th 2024

- Discussion Type
- discussion topichigher parallel transport
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Aug 30th 2024

added pointer to

- Arthur Parzygnat,
*Two-dimensional algebra in lattice gauge theory*(arXiv:1802.01139)

which provides a wealth of computational details and illustrative graphics.

- Arthur Parzygnat,

- Discussion Type
- discussion topicspectrum of a commutative ring
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topiciterated localization
- Category Latest Changes
- Started by mattecapu
- Comments 9
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topicabstract rewriting system
- Category Latest Changes
- Started by J-B Vienney
- Comments 4
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topicBirkhoff's theorem
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topicAndrew Pressley
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topicGeorge David Birkhoff
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topicBirkhoff's subdirect representation theorem
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topicBirkhoff's HSP theorem
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 30th 2024

- Discussion Type
- discussion topicsemiorthogonal decomposition
- Category Latest Changes
- Started by zskoda
- Comments 1
- Last comment by zskoda
- Last Active Aug 30th 2024