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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-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 topicEdward Witten
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by David_Corfield
- Last Active 6 days ago

added to the people-entry

*Edward Witten*a paragraph*Fields medal work*with a commented list of articles that according to Atiyah won Witten the Fields medal in 1990.

- Discussion Type
- discussion topiccubical type theory
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by nLab edit announcer
- Last Active 6 days ago

started

*cubical type theory*using a comment by Jonathan Sterling

- Discussion Type
- discussion topicJean-Claude Thomas
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 6 days ago

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

- Discussion Type
- discussion topicsimplex
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active 7 days ago

At

*simplex*I have accompanied the definition of the cellular simplex with that of the topological simplex.

- Discussion Type
- discussion topicsmooth infinity-groupoid
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Dmitri Pavlov
- Last Active 7 days ago

I am pretty much through with expanding and polishing

Now I am starting to work on

So far I have restructured the section outline at these entries to match that of the entry cohesive infinity-groupoid. All these entries are supposed to go through that list of

*Structures in a cohesive $\infty$-topos*in parallel.I have also removed at smooth infinity-groupoid a bunch of material that is meanwhile discussed in more polished form at Euclidean-topological infinity-groupoid.

To account for that I should now add a discussion of a free-forgtful adjunction between $Smooth \infty Grpd$ and $ETop \infty Grpd$ and how to transfer structure along that.

- Discussion Type
- discussion topicmonads of probability, measures, and valuations
- Category Latest Changes
- Started by PaoloPerrone
- Comments 2
- Last comment by PaoloPerrone
- Last Active 7 days ago

- Discussion Type
- discussion topiccorrespondence between measure and valuation theory
- Category Latest Changes
- Started by PaoloPerrone
- Comments 3
- Last comment by PaoloPerrone
- Last Active 7 days ago

- Discussion Type
- discussion topicGottfried Leibniz
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by David_Corfield
- Last Active 7 days ago

added pointer to

- Mikhail Katz, David Sherry,
*Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond*(arXiv:1205.0174)

where on the bottom of p. 9 I find

Leibniz rejects nilsquare and nilcube infinitesimals, which are alto-gether incompatible with his approach to differential calculus,

So if not Leibniz, who can be credited with first considering nilpotent infinitesimals?

- Mikhail Katz, David Sherry,

- Discussion Type
- discussion topicE-string
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 11th 2019

Brief idea of the

*E-string*, pointer to and snippet from one reference that makes it nicely explicit.I am compiling this and related entries because we have a clean mathematical formalization of this zoo of structures now in terms of equivariant super homotopy theory (as surveyed here). Once everything is cleaned up and published, I will try to go through all the entries and accompany the vague Idea-sections with some solid mathematics.

- Discussion Type
- discussion topictau-additive measure
- Category Latest Changes
- Started by PaoloPerrone
- Comments 6
- Last comment by PaoloPerrone
- Last Active Oct 11th 2019

- Discussion Type
- discussion topicVassiliev invariant
- Category Latest Changes
- Started by zskoda
- Comments 8
- Last comment by Urs
- Last Active Oct 10th 2019

I have reorganized somewhat entry Maxim Kontsevich (with some new links and few bits of additional info) and created a related stub Vassiliev invariant, just to record a link to an impressive online bibliography maintained by Dror Bar-Natan and Sergei Duzhin, hosted at Duzhin's webpage at Russian Academy of Sciences.

- Discussion Type
- discussion topicViktoriya Ozornova
- Category Latest Changes
- Started by Tim_Porter
- Comments 2
- Last comment by Urs
- Last Active Oct 10th 2019

- Discussion Type
- discussion topicThomason model structure
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Oct 10th 2019

Idea-section and one further reference at Thomason model structure.

I remember Mike once said on the blog somewhere that there might be some problem with Thomason's original claim that cofibrant objects in this structure are posets. I made a brief remark on this, but I can't find Mike's original comment.

- Discussion Type
- discussion topicHisao Suzuki
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 10th 2019

brief

`category:people`

-entry for hyperlinking references at*Kazama-Suzuki model*

- Discussion Type
- discussion topicYoichi Kazama
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 10th 2019

brief

`category:people`

entry for hyperlinking references at Kazama-Suzuki model

- Discussion Type
- discussion topicKazama-Suzuki model
- Category Latest Changes
- Started by nLab edit announcer
- Comments 4
- Last comment by Urs
- Last Active Oct 10th 2019

- Discussion Type
- discussion topiccanonical model structure on Cat
- Category Latest Changes
- Started by Zhen Lin
- Comments 16
- Last comment by RodMcGuire
- Last Active Oct 10th 2019

I added the remark that the canonical model structure on Cat is the model structure obtained by transferring the projective model structure on bisimplicial sets.

- Discussion Type
- discussion topicPontrjagin ring
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 10th 2019

- Discussion Type
- discussion topicWilliam Browder
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 10th 2019

brief

`category:people`

entry for hyperlinking references at*Pontrjagin product*

- Discussion Type
- discussion topicH-space
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Oct 10th 2019

I have touched

*H-space*, slightly expanded here and there and slightly reorganized it.

- Discussion Type
- discussion topicLee Neuwirth
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 9th 2019

brief

`category:people`

-entry for hyperlinking references at*configuration space of points*

- Discussion Type
- discussion topicSufian Husseini
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 9th 2019

brief

`category:people`

-entry for hyperlinking references at*configuration space of points*

- Discussion Type
- discussion topicEdward Fadell
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 9th 2019

brief

`category:people`

-entry for hyperlinking references at*configuration spaces of points*

- Discussion Type
- discussion topicAGT correspondence
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Oct 9th 2019

I have expanded the Idea-section at

*AGT correspondence*, saying more explicitly how this may be thought of as regarding the 6d (2,0)-theory as a “2d SCFT with values in 4d SYM theories” and added pointers to further references (including some reviews).I have similarly expanded/added brief remarks on AGT/generalized S-duality pointing to this at

*6d (2,0)-SCFT – Compactification on Riemann surface*and at*S-duality – for SYM – From compactification*

- Discussion Type
- discussion topicMaximilien Péroux
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Oct 9th 2019

- Discussion Type
- discussion topicKoszul duality
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Oct 9th 2019

Added

- Jonathan Beardsley, Maximilien Péroux,
*Koszul Duality in Higher Topoi*, (arXiv:1909.11724)

- Jonathan Beardsley, Maximilien Péroux,

- Discussion Type
- discussion topicclassifying space
- Category Latest Changes
- Started by Urs
- Comments 26
- Last comment by nLab edit announcer
- Last Active Oct 8th 2019

I noticed that the entry classifying space is in bad shape. I have added a table of contents and tried to structure it slightly, but much more needs to be done here.

I have added a paragraph on standard classifying spaces for topological principal bundles via the geometric realization of the simplicial space associated to the given topological group.

In the section “For crossed complexes” there is material that had been provided by Ronnie Brown which needs to be harmonized with the existing Idea-section. It proposes something like a general axiomatics on the notion of “classifying space” more than giving details on the geometric realization of crossed complexes

- Discussion Type
- discussion topicstrict 2-group
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active Oct 8th 2019

considerably expanded the entry strict 2-group.

Apart from adding an introductory discussion, and expanding the list of examples, in particular by adding that of automorphism 2-groups ...

... I in particular give the detailed translation prescription for how to encode a 2-group by a crossed module at In terms of crossed modules

This is to eventually serve as a supplement to the discussion at nonabelian group cohomology. So I spent some energy on disentangling the four different (though isomorphic) ways a crossed module gives rise to a 2-group (following my article with David Roberts).

- Discussion Type
- discussion topicBaire space
- Category Latest Changes
- Started by Mike Shulman
- Comments 15
- Last comment by Todd_Trimble
- Last Active Oct 7th 2019

I do think the phrasing “dense $G_\delta$ set (i.e. a countable intersection of dense opens)” was a bit confusing, since “i.e.” means “in other words”, but here it applies only to the immediately preceding words “$G_\delta$ set” rather than the entire phrase “dense $G_\delta$ set”. So I changed it to “dense $G_\delta$ set (i.e. a countable intersection of dense opens that is itself dense)”.