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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry beauty bundle bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched etcs fibration 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 lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure measure-theory modal modal-logic model model-category-theory 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicorbit method
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Urs
- Last Active Sep 28th 2021

I have tried to expand the Idea-section at

*orbit method*a little.

- Discussion Type
- discussion topicdifferential cohomology
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active Sep 28th 2021

I am (slowly) working on bringing the entry differential cohomology in better shape.

For the moment I am adding a section on the Hopkins-Singer formulation.

- Discussion Type
- discussion topicsheaf of spectra
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 28th 2021

stub for

*sheaf of spectra*

- Discussion Type
- discussion topicAraminta Amabel
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 28th 2021

- Discussion Type
- discussion topicequivariant group
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Sep 28th 2021

starting something, to go with and rhyme on

*equivariant principal bundle*. Not done yet, but need to save.

- Discussion Type
- discussion topicArun Debray
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 28th 2021

- Discussion Type
- discussion topicLorenzo Ramero
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 28th 2021

- Discussion Type
- discussion topic2-category
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Sep 28th 2021

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!

- Discussion Type
- discussion topicWeizhe Zheng
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 28th 2021

- Discussion Type
- discussion topicequivalence of 2-categories
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Sep 28th 2021

I have received an email asking for clarification at the (old) entry

*equivalence of 2-categories*, as to the meaning of “essentially full”. I have briefly added a parenthetical “i.e. essentially surjective on hom-categories”. But the entry deserves to be expanded a bit more, maybe somebody feels inspired to do so?

- Discussion Type
- discussion topic2-functor
- Category Latest Changes
- Started by Alec Rhea
- Comments 12
- Last comment by Urs
- Last Active Sep 28th 2021

- Discussion Type
- discussion topicRobert Gordon
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 28th 2021

brief

`category:people`

-entry for hyperlinking references at*tricategory*

- Discussion Type
- discussion topicAntonio Gómez-Tato
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 27th 2021

brief

`category:people`

-entry for hyperlinking references at*Borel-equivariant rational homotopy theory*

- Discussion Type
- discussion topicBorel-equivariant rational homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 27th 2021

- Discussion Type
- discussion topicfuzzy dark matter
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Sep 27th 2021

Added to the entry

*fuzzy dark matter*pointer to Lee 17 which appeared today on the preprint server. This is just a concise 2.5 page survey of all the available literature, but as such is very useful. For instance it points out this Nature-article:- Hsi-Yu Schive, Tzihong Chiueh, Tom Broadhurst,
*Cosmic structure as the quantum interference of a coherent dark wave*, Nature Physics 10, 496–499 (2014) (doi:10.1038/nphys2996)

which presents numerical simulation of the fuzzy dark matter model compared to experimental data.

- Hsi-Yu Schive, Tzihong Chiueh, Tom Broadhurst,

- Discussion Type
- discussion topicdouble bicategory
- Category Latest Changes
- Started by John Baez
- Comments 6
- Last comment by Tim_Porter
- Last Active Sep 27th 2021

- I started a little page called double bicategory.

- Discussion Type
- discussion topicrepresentable 2-category
- Category Latest Changes
- Started by varkor
- Comments 4
- Last comment by varkor
- Last Active Sep 26th 2021

- Discussion Type
- discussion topicBrown representability theorem
- Category Latest Changes
- Started by Mike Shulman
- Comments 14
- Last comment by Urs
- Last Active Sep 26th 2021

Thanks to Karol Szumiło’s answer to my MO question, I have added to Brown representability theorem a mention of the counterexamples for nonconnected pointed spaces and for unpointed spaces (plus a mention of Brown’s abstract categorical version).

Next task: fix the utterly horrific wikipedia page. (Edit: done!)

- Discussion Type
- discussion topicfundamental theorem of dg-algebraic rational homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Sep 26th 2021

- Discussion Type
- discussion topicJohn Stillwell
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 26th 2021

- Discussion Type
- discussion topicAnalysis Situs
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 26th 2021

- Discussion Type
- discussion topicidempotent monoid in a monoidal category
- Category Latest Changes
- Started by Théo de Oliveira S.
- Comments 9
- Last comment by Théo de Oliveira S.
- Last Active Sep 25th 2021

Page created. Idempotent monoids should be to monoids as idempotent monads are to monads.

I’ve added the examples of idempotent elements in (ordinary) monoids (1), idempotent morphisms in categories (2), solid rings (3), idempotent monads (4), idempotent $1$-morphisms in bicategories (5), and “solid ring spectra” (6) ―What are other examples?

Also, should idempotent monoids have a unit? The examples 1 and 2 I mentioned above don’t, but 3, 4, and 6 do, while whether 5 does or doesn’t seems to vary a bit among the literature (AFAIU).

- Discussion Type
- discussion topicSamson Abramsky
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Sep 25th 2021

Added writing here

- Maximilian Doré, Samson Abramsky,
*Towards Simplicial Complexes in Homotopy Type Theory*(pdf)

- Maximilian Doré, Samson Abramsky,

- Discussion Type
- discussion topicsimplicial complex
- Category Latest Changes
- Started by Todd_Trimble
- Comments 37
- Last comment by David_Corfield
- Last Active Sep 25th 2021

Made some edits and additions at simplicial complex.

- Discussion Type
- discussion topicStandard Conjectures on Algebraic Cycles
- Category Latest Changes
- Started by Mateo Carmona
- Comments 1
- Last comment by Mateo Carmona
- Last Active Sep 25th 2021

- Discussion Type
- discussion topicdomain specific embedded programming language
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by nLab edit announcer
- Last Active Sep 25th 2021

Roux Cody kindly alerted me of the fact that analog of synthetic mathematics under “computational trinitarianism” in programming theory is that of

*domain specific embedded programming languages*. To record this neat insight I have now created a minimum entry on the latter and cross-linked a bit.

- Discussion Type
- discussion topicSL(2,H)
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 25th 2021

- Discussion Type
- discussion topicLie group
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Corbin
- Last Active Sep 24th 2021

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 topicMisha Gavrilovich
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 24th 2021

added “Selected writings”:

Misha Gavrilovich,

*Point set topology as diagram chasing computations*, The De Morgan Gazette. 2014. Vol. 5. No. 4. P. 23-32. (arXiv:1408.6710, pdf)Misha Gavrilovich,

*The unreasonable power of the lifting property in elementary mathematics*, 2017 (arXiv:1707.06615, pdf)

- Discussion Type
- discussion topicseparation axioms
- Category Latest Changes
- Started by maxsnew
- Comments 6
- Last comment by nLab edit announcer
- Last Active Sep 24th 2021

The table on the separation axioms page looks very messed up. If I open the table directly at main separation axioms – table it looks fine but on the separation axioms page, all of the links are gone. How do we fix it?

- Discussion Type
- discussion topicspectral super-scheme
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 24th 2021

I have added pointers to Mikhail Kapranov’s talks on the sphere spectrum in relation to super-algebra, and added some words at the beginning that this was the original motivation for the proposed definition of spectral supergeometry in the entry.

Also I fixed the link to the video recording of Krapranov’s 2013 talk. The previous link no longer worked but there is a YouTube copy of the video. Fixed this also at

*superalgebra*, see there at Kaprananov 13

- Discussion Type
- discussion topicperiodic table
- Category Latest Changes
- Started by John Baez
- Comments 4
- Last comment by Richard Williamson
- Last Active Sep 24th 2021

- Discussion Type
- discussion topicreal homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 23rd 2021

created a minimum at

*real homotopy theory*

- Discussion Type
- discussion topicHandbook of Algebraic Topology
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Sep 23rd 2021

- Discussion Type
- discussion topicMP
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Sep 23rd 2021

- Discussion Type
- discussion topiclocally compact topological space
- Category Latest Changes
- Started by Urs
- Comments 64
- Last comment by Urs
- Last Active Sep 23rd 2021

I gave

*locally compact topological space*an Idea-section and added the other equivalent definition (here).

- Discussion Type
- discussion topiccore of a ring
- Category Latest Changes
- Started by Urs
- Comments 17
- Last comment by Urs
- Last Active Sep 23rd 2021

gave

*core of a ring*some minimum content

- Discussion Type
- discussion topiceven cohomology theory
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by Urs
- Last Active Sep 23rd 2021

- Discussion Type
- discussion topicRobert H. Szczarba
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 23rd 2021

brief

`category:people`

-entry for hyperlinking references at*real homotopy theory*and*continuous cohomology*

- Discussion Type
- discussion topicstrong monad
- Category Latest Changes
- Started by Sam Staton
- Comments 21
- Last comment by mattecapu
- Last Active Sep 23rd 2021

- Discussion Type
- discussion topicDavid Mehrle
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 23rd 2021

- Discussion Type
- discussion topicRenzo A. Piccinini
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 22nd 2021

- Discussion Type
- discussion topicshape via cohesive path ∞-groupoid
- Category Latest Changes
- Started by Urs
- Comments 40
- Last comment by Urs
- Last Active Sep 22nd 2021

I have added pointer to the arXiv copy to the item

- Daniel Berwick-Evans, Pedro Boavida de Brito, Dmitri Pavlov,
*Classifying spaces of infinity-sheaves*(arXiv:1912.10544)

- Daniel Berwick-Evans, Pedro Boavida de Brito, Dmitri Pavlov,

- Discussion Type
- discussion topicslice theorem
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Sep 22nd 2021

- Discussion Type
- discussion topictopological G-space
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Sep 22nd 2021

added pointer to Bredon 72. Will add this pointer also to various related entries on equivariant homotopy theory

- Discussion Type
- discussion topicK-orientation
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 22nd 2021

- Discussion Type
- discussion topicclassifying space
- Category Latest Changes
- Started by Urs
- Comments 39
- Last comment by Urs
- Last Active Sep 22nd 2021

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 topicBorel construction
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Sep 22nd 2021

started an entry on the

*Borel construction*, indicating its relation to the nerve of the action groupoid.

- Discussion Type
- discussion topicfive lemma
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Sep 22nd 2021

touched

*five lemma*

- Discussion Type
- discussion topichomological category
- Category Latest Changes
- Started by zskoda
- Comments 7
- Last comment by Urs
- Last Active Sep 22nd 2021

New entry homological category.

- Discussion Type
- discussion topicregular category
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Sep 22nd 2021

added publication details for this reference:

- F. Cagliari, S. Mantovani, Enrico Vitale,
*Regularity of the category of Kelley spaces*, Applied Categorical Structures volume 3, pages 357–361 (1995) (doi:10.1007/BF00872904, pdf)

and am copying it over to

*compactly generated topological space*, too- F. Cagliari, S. Mantovani, Enrico Vitale,

- Discussion Type
- discussion topicprotomodular category
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by Urs
- Last Active Sep 22nd 2021

I added some content in protomodular category. It’s mostly drawn from Bourn’s papers. It will need brushing up, cross-linking, etc.

There are many further related concepts. Don’t know how important they are, e.g., Bourn says

The dual of a topos is arithmetical.

Is that a standard concept? And ’affine categories’?

- Discussion Type
- discussion topicMalcev category
- Category Latest Changes
- Started by Keith Harbaugh
- Comments 6
- Last comment by Urs
- Last Active Sep 22nd 2021

- Discussion Type
- discussion topicTamar Janelidze
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 22nd 2021

- Discussion Type
- discussion topicMalcev, protomodular, homological and semi-abelian categories
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 22nd 2021

- Discussion Type
- discussion topichomotopy theory
- Category Latest Changes
- Started by Tim_Porter
- Comments 46
- Last comment by Urs
- Last Active Sep 22nd 2021

I have deleted an old out of date query box from homotopy theory.

- Discussion Type
- discussion topicSabrina Pasterski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 22nd 2021

brief

`category:people`

-entry for hyperlinking references at*celestial amplitudes*

- Discussion Type
- discussion topicflat space holography
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Sep 22nd 2021

- Discussion Type
- discussion topicDaniel Grumiller
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Sep 22nd 2021

brief

`category:people`

-entry for hyperlinking references at*flat space holography*

- Discussion Type
- discussion topicequality
- Category Latest Changes
- Started by Urs
- Comments 43
- Last comment by Urs
- Last Active Sep 21st 2021

I was involved in some discussion about where the word “intensional” as in “intensional equality” comes from and how it really differs from “intenTional” and what the point is of having such a trap of terms.

Somebody dug out Martin-Löf’s lecture notes “Intuitionistic type theory” from 1980 to check. Having it in front of me and so before I forget, I have now briefly made a note on some aspects at

*equality*in the section*Different kinds of equalits*(below the first paragraph which was there before I arrived.)Anyway, on p. 31 Martin-Löf has

intensional (sameness of meaning)

I have to say that the difference between “sameness of meaning” and “sameness of intenTion”, if that really is the difference one wants to make, is at best subtle.