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- Discussion Type
- discussion topic2-vector space
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Tim_Porter
- Last Active Oct 23rd 2021

- Discussion Type
- discussion topicAdS-CFT
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by David_Corfield
- Last Active Oct 22nd 2021

- Discussion Type
- discussion topicholography as Koszul duality
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Oct 22nd 2021

- Discussion Type
- discussion topiccommutative monoid
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Oct 22nd 2021

added missing pointer to

*commutative monoid in a symmetric monoidal category*

- Discussion Type
- discussion topicprofunctor
- Category Latest Changes
- Started by Mike Shulman
- Comments 26
- Last comment by Urs
- Last Active Oct 21st 2021

How would people feel about renaming distributor to profunctor? I seem to recall that when this came up on the Cafe, I was the main proponent of the former over the latter, and I've since changed my mind.

- Discussion Type
- discussion topicProf
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 21st 2021

- Discussion Type
- discussion topicMaren Justesen
- Category Latest Changes
- Started by varkor
- Comments 3
- Last comment by Urs
- Last Active Oct 21st 2021

- Discussion Type
- discussion topicReedy model structure
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by mbid
- Last Active Oct 21st 2021

- Discussion Type
- discussion topicAnders Kock
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active Oct 21st 2021

- Discussion Type
- discussion topicgeneral relativity
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Oct 21st 2021

I wanted to be able to use the link without it appearing in grey, so I created a stub for general relativity.

- Discussion Type
- discussion topic2-type theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 10
- Last comment by Urs
- Last Active Oct 21st 2021

- Discussion Type
- discussion topiccategory with duals
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by mattecapu
- Last Active Oct 21st 2021

I see that Peter Selinger edited and added material to category with duals

- Discussion Type
- discussion topicnucleosynthesis
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Oct 21st 2021

- Discussion Type
- discussion topicToshitaka Kajino
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 20th 2021

- Discussion Type
- discussion topicJames Alvey
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 20th 2021

brief

`category:people`

-entry for hyperlinking references at*primordial nucleosynthesis*

- Discussion Type
- discussion topiclax (∞,1)-colimit
- Category Latest Changes
- Started by Hurkyl
- Comments 9
- Last comment by Hurkyl
- Last Active Oct 20th 2021

I added the description of lax (co)limits of Cat-valued functors via (co)ends and ordinary (co)limits. I should probably flesh this out more.

I’ve adopted the convention on twisted arrows at twisted arrow category, which is opposite of that in GNN.

In the case of ordinary 2-category, when the diagram category is a 1-category, is the expression of lax (co)limits via ordinary weighted (co)limits really as simple as taking the weights $C_{\bullet/}$ or $C_{/\bullet}$? I can’t find a reference that spells that out clearly; if there really is such a simple description it should be put on the lax (co)limit page.

- Discussion Type
- discussion topicspan
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active Oct 20th 2021

Changes made only to the Universal property of the 2-category of spans section. The citations by Urs lead to another citation which, in turn, leads to another citation. With a little effort, I tracked down the a full copy of said universal property, I’ve replicated it here, added the citation used, although I left the previous citations there for convenience; a more experienced editor can remove those if they would like.

I would like to note that the author whose work I have referenced, Hermida, also notes: “[this universal property] is folklore although we know no references for it.”

Please make any corrections needed and clean up the language here; this is a fairly direct copy of what is written, but I imagine somebody with more knowledge of all the language used here can rewrite this universal property stuff in a cleaner way.

Thanks!

Anonymous

- Discussion Type
- discussion topicMarzia Bordone
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 20th 2021

- Discussion Type
- discussion topicanomalous magnetic moment
- Category Latest Changes
- Started by Urs
- Comments 27
- Last comment by Urs
- Last Active Oct 20th 2021

there is an old article (Berends-Gastman 75) that computes the 1-loop corrections due to perturbative quantum gravity to the anomalous magnetic moment of the electron and the muon. The result turns out to be independent of the choice of (“re”-)normalization (hence what they call “finite”).

I have added a remark on this in the $(g-2)$-entry here and also at

*quantum gravity*here.

- Discussion Type
- discussion topicinjection
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 20th 2021

Moving the following old query out of the entry to here. Maybe it inspires somebody to add to the entry a remark towards the answer:

[ begin forwarded query ]

+– {: .query} Anonymous: Under what conditions are all injections in a category monomorphisms? Obviously injections are monomorphisms in a well-pointed topos or pretopos (those are models of particular types of set theories), but does that remain true in a (pre)topos without well-pointedness, a coherent category or an exact category?

Anonymous: There is this stackexchange post, but the answers only refer to concrete categories with a forgetful functor to Set and a free functor from Set, rather than arbitrary abstract categories. =–

[ end forwarded query ]

- Discussion Type
- discussion topicinjective-on-objects functor
- Category Latest Changes
- Started by varkor
- Comments 2
- Last comment by Urs
- Last Active Oct 20th 2021

- Discussion Type
- discussion topicrigid monoidal category
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Oct 19th 2021

Added:

### Free rigid monoidal categories

The inclusion of the 2-category of monoidal categories into the 2-category of rigid monoidal categories admits a left 2-adjoint functor $L$.

Furthermore, the unit of the adjunction is a strong monoidal fully faithful functor, i.e., any monoidal category $C$ admits a fully faithful strong monoidal functor $C\to L(C)$, where $L(C)$ is a rigid monoidal category.

See Theorems 1 and 2 in Delpeuch \cite{Delpeuch}.

- Antonin Delpeuch,
*Autonomization of monoidal categories*, arXiv, doi.

- Antonin Delpeuch,

- Discussion Type
- discussion topicmain separation axioms -- as lifting properties
- Category Latest Changes
- Started by nLab edit announcer
- Comments 8
- Last comment by nLab edit announcer
- Last Active Oct 19th 2021

A page with diagrams representing separation axioms T0-T4 as lifting properties, to be included into the separation axioms.

Anonymous

- Discussion Type
- discussion topicproperties of functors -- contents
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by varkor
- Last Active Oct 19th 2021

- Discussion Type
- discussion topicduality between algebra and geometry
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 11
- Last comment by Dmitri Pavlov
- Last Active Oct 19th 2021

- Discussion Type
- discussion topicHausdorff space
- Category Latest Changes
- Started by Mike Shulman
- Comments 11
- Last comment by Urs
- Last Active Oct 19th 2021

I added some discussion to Hausdorff space of how the localic and spatial versions compare in classical and constructive mathematics, including in particular the fact that I just learned (in discussion with Martin Escardo and Andrej Bauer) that a discrete locale is Hausdorff iff it has decidable equality.

- Discussion Type
- discussion topicMatti Järvinen
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 19th 2021

brief

`category:people`

-entry for hyperlinking references at*holographic QCD*and*neutron star*

- Discussion Type
- discussion topicmeasurable field of Hilbert spaces
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 5
- Last comment by DavidRoberts
- Last Active Oct 19th 2021

Created:

## Idea

A

**measurable field of Hilbert spaces**is the exact analogue of a vector bundle over a topological spaces in the setting of bundles of infinite-dimensional Hilbert spaces over measurable spaces.## Definition

The original definition is due to John von Neumann (Definition 1 in \cite{Neumann}).

We present here a slightly modernized version, which can be found in many modern sources, e.g., Takesaki \cite{Takesaki}.

\begin{definition} Suppose $(X,\Sigma)$ is a measurable space equipped with a σ-finite measure $\mu$, or, less specifically, with a σ-ideal $N$ of negligible subsets so that $(X,\Sigma,N)$ is an enhanced measurable space. A

**measurable field of Hilbert spaces**over $(X,\Sigma,N)$ is a family $H_x$ of Hilbert spaces indexed by points $x\in X$ together with a vector subspace $M$ of the product $P$ of vector spaces $\prod_{x\in X} H_x$. The elements of $M$ are known as**measurable sections**. The pair $(\{H_x\}_{x\in X},M)$ must satisfy the following conditions. * For any $m\in M$ the function $X\to\mathbf{R}$ ($x\mapsto \|m(x)\|$) is a measurable function on $(X,\Sigma)$. * If for some $p\in P$, the function $X\to\mathbf{C}$ ($x\mapsto\langle p(x),m(x)\rangle$) is a measurable function on $(X,\Sigma)$ for any $m\in M$, then $p\in M$. * There is a countable subset $M'\subset M$ such that for any $x\in X$, the closure of the span of vectors $m(x)$ ($m\in M'$) coincides with $H_x$. \end{definition}The last condition restrict us to bundles of separable Hilbert spaces. One can also define bundles of nonseparable Hilbert spaces, but this cannot be done simply by dropping the last condition.

## Serre–Swan-type duality

The category of measurable fields of Hilbert spaces on $(X,\Sigma,N)$ is equivalent to the category of W*-modules over the commutative von Neumann algebra $\mathrm{L}^\infty(X,\Sigma,N)$.

(If we work with bundles of separable Hilbert spaces, then W*-modules must be countably generated.)

## Related entries

## References

\bibitem{Neumann} John Von Neumann,

*On Rings of Operators. Reduction Theory*, The Annals of Mathematics 50:2 (1949), 401. doi.\bibitem{Takesaki} Masamichi Takesaki,

*Theory of Operator Algebras. I*, Springer, 1979.

- Discussion Type
- discussion topicIsbell duality - table
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Oct 19th 2021

the table didn’t have the basic examples, such as

*Gelfand duality*and*Milnor’s exercise*. Added now.

- Discussion Type
- discussion topiclambda theory
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Oct 19th 2021

Filled in publication details for

- {#Hyland13} Martin Hyland.
*Classical lambda calculus in modern dress*Mathematical Structures in Computer Science, 27(5) (2017) 762-781. doi:10.1017/S0960129515000377. arxiv:1211.5762

- {#Hyland13} Martin Hyland.

- Discussion Type
- discussion topiclambda-calculus
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active Oct 18th 2021

- Discussion Type
- discussion topicreflexive object
- Category Latest Changes
- Started by Noam_Zeilberger
- Comments 3
- Last comment by DavidRoberts
- Last Active Oct 18th 2021

A while ago I created reflexive object without too much content, and now I’ve revised and expanded it a bit (after hearing an inspiring talk by Dana Scott!).

- Discussion Type
- discussion topicArtin gluing
- Category Latest Changes
- Started by Todd_Trimble
- Comments 14
- Last comment by nLab edit announcer
- Last Active Oct 18th 2021

Some stuff that Zoran wrote on recollement reminded me that I had been long meaning to write Artin gluing, which I’ve done, starting in a kind of pedestrian way (just with topological spaces). Somewhere in the section on the topos case I mention a result to be found in the Elephant which I couldn’t quite find; if you know where it is, please let me know.

- Discussion Type
- discussion topicaffine scheme
- Category Latest Changes
- Started by IngoBlechschmidt
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active Oct 18th 2021

At

*affine scheme*, the fundamental theorem on morphisms of schemes was stated the other way round. I fixed that.As a handy mnemonic, here is a quick and down-to-earth way to see that the claim “$Sch(Spec R, Y) \cong CRing(\mathcal{O}_Y(Y), R)$” is wrong. Take $Y = \mathbb{P}^n$ and $R = \mathbb{Z}$. Then the left hand side consists of all the $\mathbb{Z}$-valued points of $\mathbb{P}^n$. On the other hand, the right hand side only contains the unique ring homomorphism $\mathbb{Z} \to \mathbb{Z}$, since $\mathcal{O}_{\mathbb{P}^n}(\mathbb{P}^n) \cong \mathbb{Z}$.

- Discussion Type
- discussion topicembedding of smooth manifolds into formal duals of R-algebras
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active Oct 18th 2021

I finally gave this statement its own entry, in order to be able to conveniently point to it:

*embedding of smooth manifolds into formal duals of R-algebras*

- Discussion Type
- discussion topicsymplectic duality
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by David_Corfield
- Last Active Oct 18th 2021

Ben Webster created

*symplectic duality*.See his message at the $n$Café here.

- Discussion Type
- discussion topicAlexei Pirkovskii
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 18th 2021

brief

`category:people`

-entry for hyperlinking references at*EFC-algebra*

- Discussion Type
- discussion topicgroup cohomology
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by nLab edit announcer
- Last Active Oct 18th 2021

added to group cohomology

in the section structured group cohomology some remarks about how to correctly define Lie group cohomology and topological group cohomology etc. and how not to

in the section Lie group cohiomology a derivation of how from the right oo-categorical definition one finds after some unwinding the correct definition as given in the article by Brylinski cited there.

it's late here and I am now in a bit of a hurry to call it quits, so the proof I give there may need a bit polishing. I'll take care of that later...

- Discussion Type
- discussion topicEFC-algebra
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 2
- Last comment by Urs
- Last Active Oct 18th 2021

Created:

## Definition

An

$CartHolo \to Set,$**entire functional calculus algebra**is a product-preserving functorwhere $CartHolo$ is the category of finite-dimensional complex vector spaces and holomorphic maps.

This is in complete analogy to C^∞-rings, and EFC-algebras are applicable in similar contexts.

## Properties

The category of globally finitely presented Stein spaces is contravariantly equivalent to the category of finitely presented EFC-algebras. The equivalence functor sends a Stein space to its EFC-algebra of global sections.

The category of Stein spaces of finite embedding dimension is contravariantly equivalent to the category of finitely generated EFC-algebras. The equivalence functor sends a Stein space to its EFC-algebra of global sections.

These statements can thus be rightfully known as

**Stein duality**.## Related concepts

## References

Alexei~Yu.~Pirkovskii, Holomorphically finitely generated algebras. Journal of Noncommutative Geometry 9 (2015), 215–264. arXiv:1304.1991, doi:10.4171/JNCG/192.

J.~P.~Pridham, A differential graded model for derived analytic geometry. Advances in Mathematics 360 (2020), 106922. arXiv:1805.08538v1, doi:10.1016/j.aim.2019.106922.

- Discussion Type
- discussion topicStonean space
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 2
- Last comment by Dmitri Pavlov
- Last Active Oct 18th 2021

- Discussion Type
- discussion topiclocalizable Boolean algebra
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Oct 18th 2021

Created:

## Idea

A Boolean algebra is

*localizable*if it admits “sufficiently many” measures.## Definition

A

**localizable Boolean algebra**is a complete Boolean algebra $A$ such that $1\in A$ equals the supremum of all $a\in A$ such that the Boolean algebra $aA$ admits a faithful continuous valuation $\nu\colon A\to[0,1]$. Here a valuation $\nu\colon A\to[0,\infty]$ is faithful if $\nu(a)=0$ implies $a=0$.A

**morphism of localizable Boolean algebras**is a complete (i.e., suprema-preserving) homomorphism of Boolean algebras.## Properties

The category of localizable Boolean algebras admits all small limits and small colimits.

It is equivalent to the category of commutative von Neumann algebras.

The equivalence sends a commutative von Neumann algebra to its localizable Boolean algebra of projections. It sends a localizable Boolean algebra $A$ to the complexification of the completion of the free real algebra on $A$, given by the left adjoint to the functor that takes idempotents.

## Related concepts

## References

- Dmitri Pavlov, Gelfand-type duality for commutative von Neumann algebras. Journal of Pure and Applied Algebra 226:4 (2022), 106884. doi:10.1016/j.jpaa.2021.106884](https://doi.org/10.1016/j.jpaa.2021.106884), arXiv:2005.05284.

- Discussion Type
- discussion topicGrothendieck topos
- Category Latest Changes
- Started by JonasFrey
- Comments 28
- Last comment by Urs
- Last Active Oct 18th 2021

On the page Grothendieck topos, Toby Bartels raised the question whether local smallness should be part of the Giraud axioms, referring to a math overflow discussion on a related issue. A while ago I added some comments to the math overflow discussion saying that local smallness

*has*to be part of the Giraud axioms, giving an argument with universes, but nobody seems to have noticed. I raise the issue here again since it’s beside the point of the original math overflow discussion, but clearly related to the nlab.Concretely, if U, V are universes with U in V, then V is not a Grothendieck topos relative to U, but satisfies all the conditions of the Giraud axioms.

The confusion on math overflow seems to come from C2.2.8(vii) in the Elephant, where Grothendieck toposes are characterized as infty-pretoposes with a generating set of objects.

The crucial point is that the assumption of local smallness is implicit in the definition of infty-pretopos in the Elephant, but not in the nlab.

To actually see that one has to look fairly closely at the Elephant:

Before Lemma A.1.4.19, Johnstone writes ” … C is an infty-pretopos if it is an infty-positive geometric category which is effective as a regular category.

a geometric category is defined as one “satisfying the conditions of Lemma 1.4.18”, which can be reformulated as “regular well-powered with pullback-stable small joins of subobjects”.

So geometric categories are well-powered, but any regular well powered category is also locally small, since Hom(A,B) can be embedded into sub(AxB) via graphs.

On the other hand, well poweredness is not a requirement for geometric categories on the nlab.

I also prefer the convention on the nlab, since there are certain interesting settings where we don’t have well-poweredness, and then it is possible to have small joins of subobjects w/o having small meets.

But this means that the Giraud theorem on the nlab has to contain the assumption of local smallness explicitely.

I will now go ahead and remove the comments of Toby Bartels and add the condition. Feel free and rollback or modify if you don’t agree.

(By the way, my favourite definition of infty-pretopos is “exact, infty-extensive category”. I find this easier to digest and memorize)

- Discussion Type
- discussion topiccategory of sheaves
- Category Latest Changes
- Started by Urs
- Comments 31
- Last comment by Urs
- Last Active Oct 18th 2021

polished category of sheaves slightly

- Discussion Type
- discussion topiccategorical homotopy groups in an (infinity,1)-topos
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 18th 2021

I have touched the first paragraphs of the Definition section (here) for formatting, and added more explicit pointer to

*Powering of $\infty$-toposes over $\infty$-groupoids*.More could be done to improved this old entry…

- Discussion Type
- discussion topicpowering of ∞-toposes over ∞-groupoids -- section
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 18th 2021

a bare sub-section, to be

`!include`

-ed inside the Properties-section of into relevant entries (such as at*powering*and at*(infinity,1)-topos*), see also the thread here

- Discussion Type
- discussion topicpowering
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 18th 2021

I brushed up the entry power a bit: wrote an Idea-section, created an Examples-section etc.

- Discussion Type
- discussion topicterminal geometric morphism
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 18th 2021

I keep wanting to point to properties of the terminal geometric morphism. While we had this scattered around in various entries (such as at

*global sections*, at*(infinity,1)-topos*and elsewhere – but not for instance at*(infinity,1)-geometric morphism*) I am finally giving it its own entry, for ease of hyperlinking.So far this contains the (elementary) proofs that the geometric morphism to the base $Set$/$Grpd_\infty$ is indeed essentially unique, and that the right adjoint is equivalently given by homs out of the terminal object.

- Discussion Type
- discussion topicheavy flavor hadrodynamics via holographic QCD -- references
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 18th 2021

a bare list of references, to be

`!include`

-ed into relevant entries (such as*AdS/QCD correspondence*and*heavy flavor*)

- Discussion Type
- discussion topictimed set
- Category Latest Changes
- Started by Corbin
- Comments 1
- Last comment by Corbin
- Last Active Oct 17th 2021

- Discussion Type
- discussion topiccomplexity class
- Category Latest Changes
- Started by Corbin
- Comments 3
- Last comment by Corbin
- Last Active Oct 17th 2021

- Discussion Type
- discussion topicresolution of singularities
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Oct 17th 2021

added pointer to

Heisuke Hironaka,

*Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I*, Annals of Mathematics Second Series, Vol. 79, No. 1 (Jan., 1964), pp. 109-203 (95 pages) (jstor:1970486)Michael Atiyah,

*Resolution of singularities and Division of Distributions*, Communications in Pure and Applied Mathematics, vol. XXIII, 145-150 (1970)

with some comment

- Discussion Type
- discussion topicsuperspace
- Category Latest Changes
- Started by Urs
- Comments 23
- Last comment by David_Corfield
- Last Active Oct 17th 2021

completed publication data for:

- Abdus Salam, John Strathdee,
*Superfields and Fermi-Bose symmetry*, Physical Review D11, 1521-1535 (1975) (doi:10.1142/9789812795915_0051)

- Abdus Salam, John Strathdee,

- Discussion Type
- discussion topicκ-ary exact category
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by Urs
- Last Active Oct 17th 2021

Removed the requirement (under [https://ncatlab.org/nlab/revision/%CE%BA-ary+exact+category/15#examples_2](§ Examples)) that infinitary-coherent categories and infinitary pretopoi be well-powered (since the corresponding

- Discussion Type
- discussion topicHenri Cartan
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 17th 2021

added pointer to:

- John Frank Adams,
*The work of M. H. Cartan in its relation with homotopy theory*, Colloque analyse et topologie,Astérisque no. 32-33 (1976), p. 29-41 (numdam:AST_1976__32-33__29_0/)

- John Frank Adams,

- Discussion Type
- discussion topicprincipal bundle
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Oct 17th 2021

I have added to

*principal bundle*a remark on their

*definition*As quotients;statements about (classes of) (counter-)examples of quotients

Thanks for pointers to the literature from this MO thread!

- Discussion Type
- discussion topicequivariant localization
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by Urs
- Last Active Oct 17th 2021

equivariant localization (only good references and links for now) and Michael Atiyah

- Discussion Type
- discussion topicequivariant de Rham cohomology
- Category Latest Changes
- Started by Urs
- Comments 22
- Last comment by Urs
- Last Active Oct 17th 2021

created

*equivariant de Rham cohomology*with a brief note on the Cartan model.(I seem to remember that we had discussion of this in the general context of Lie algebroids elsewhere already, several years back. But now I cannot find it….)

- Discussion Type
- discussion topicseparation axioms
- Category Latest Changes
- Started by maxsnew
- Comments 7
- Last comment by nLab edit announcer
- Last Active Oct 16th 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 topicequivariant cohomology
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 16th 2021

I have removed the bulk of the Idea section that I had written, starting way back when the entry was created in 2013.

I kept the other material that Mike (Shulman) had written.

I see now that mine was really besides the point.

Now that I finally understand this topic more deeply, maybe I find time to write a better explanation of what’s really going on.

- Discussion Type
- discussion topicnatural number
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by Urs
- Last Active Oct 16th 2021