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- Discussion Type
- discussion topiccompact space
- Category Latest Changes
- Started by Todd_Trimble
- Comments 86
- Last comment by Mike Shulman
- Last Active 3 days ago

As an outcome of recent discussion at Math Overflow here, Mike Shulman suggested some nLab pages where comparisons of different definitions of compactness are rigorously established. I have created one such page: compactness and stable closure. (The importance and significance of the stable closure condition should be brought out better.)

- Discussion Type
- discussion topicmodal homotopy type theory
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 3 days ago

copied over the homotopy-theoretic references from

*modal type theory*to here.

- Discussion Type
- discussion topicflavour anomaly
- Category Latest Changes
- Started by Urs
- Comments 133
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicNiels Tuning
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

brief

`category:people`

-page for hyperlinking references at*flavour anomaly*and at*LHCb experiment*

- Discussion Type
- discussion topicHopf-Galois extension
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active 3 days ago

Added a reference

- John Rognes,
*Galois extensions of structured ring spectra/Stably dualizable groups*, Memoires of the American Mathematical Society, 192(898), 2008, partly available as (pdf)

- John Rognes,

- Discussion Type
- discussion topicétale space
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 26
- Last comment by Dmitri Pavlov
- Last Active 3 days ago

Corrected the spelling.

In English, “étale” in “étale space” is definitely an adjective, not a past participle (otherwise it would be “étaled space”).

The last “e” is always silent in the English pronunciation, so cannot be an “é”.

This also matches the usage in the literature.

- Discussion Type
- discussion topicatlas
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

I have removed the few stub lines that were in this entry before, and wrote out a more informative Idea-section. Currently it reads as follows:

In basic topology and differential geometry, by an

*atlas*of/for a topological-, differentiable- or smooth manifold $X$ one means a collection of coordinate charts $U_i \subset X$ which form an open cover of $X$.If one considers here the disjoint union $\mathcal{U} \coloneqq \underset{i}{\sqcup} U_i$ of all the choordinate charts, then the separate chart embeddings $U_i \subset X$ give rise to a single map (continuous/differentiable function)

$\mathcal{U} \longrightarrow X$and now the condition for an atlas is that this is a surjective étale map/local diffeomorphism.

If, next, one regards this morphism, under the Yoneda embedding, inside the topos of formal smooth sets, then these conditions on an atlas say that this morphism is

In this abstract form the concept of an atlas generalizes to any cohesive higher geometry (KS 17, Def. 3.3, Wellen 18, Def 4.13).

Next, for a geometric stack $\mathcal{X}$, an atlas is a smooth manifold $\mathcal{U}$ (for differentiable stacks) or scheme $\mathcal{U}$ (for algebraic stacks) or similar, equipped with a morphism

$\mathcal{U} \longrightarrow \mathcal{X}$that is an effective epimorphism and formally étale morphism in the corresponding higher topos (for instance in that of formal smooth infinity-groupoids).

Here the terminology has a bifurcation:

In the general context of geometric stacks one typically drops the second condition and calls any effective epimorphism from a smooth manifold or scheme to a differentiable stack or algebraic stack, respectively, an

*atlas*.If in addition the condition is imposed that such an effective epimorphism exists which is also formally étale, then the geometric stack is called an

*orbifold*or*Deligne-Mumford stack*(often with various further conditions imposed).

- Discussion Type
- discussion topiccocomplete category
- Category Latest Changes
- Started by maxsnew
- Comments 1
- Last comment by maxsnew
- Last Active 4 days ago

- Discussion Type
- discussion topiccentral extension
- Category Latest Changes
- Started by Richard Williamson
- Comments 3
- Last comment by David_Corfield
- Last Active 4 days ago

- Discussion Type
- discussion topictensor meson
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicIsabelle
- Category Latest Changes
- Started by zskoda
- Comments 4
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicgeneralized Scherk-Schwarz reduction
- Category Latest Changes
- Started by Luigi
- Comments 2
- Last comment by Luigi
- Last Active 4 days ago

- Discussion Type
- discussion topicAdam Lewandowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicMatthew Schwartz
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicEdvard Musaev
- Category Latest Changes
- Started by Luigi
- Comments 2
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicgauged supergravity
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

have added some further reference at

*gauged supergravity*and related entries.

- Discussion Type
- discussion topicglueball
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicPeter Minkowski
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicHarald Fritzsch
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 4 days ago

- Discussion Type
- discussion topicGUT
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active 4 days ago

**Edit to**: GUT by Urs Schreiber at 2018-04-01 01:21:13 UTC.**Author comments**:added pointer to textbook account

- Discussion Type
- discussion topicFreund-Rubin compactification
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicobject-oriented programming
- Category Latest Changes
- Started by AlexisHazell
- Comments 56
- Last comment by David_Corfield
- Last Active 5 days ago

- Discussion Type
- discussion topicL-infinity algebras in physics
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 5 days ago

added pointer to these two recent references, identifying further $L_\infty$-algebra structure in Feynman amplitudes/S-matrices of perturbative quantum field theory:

Markus B. Fröb,

*Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories*(arXiv:1803.10235)Alex Arvanitakis,

*The $L_\infty$-algebra of the S-matrix*(arXiv:1903.05643)

- Discussion Type
- discussion topicembedding tensor
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Luigi
- Last Active 5 days ago

- Discussion Type
- discussion topicembedding tensors and tensor hierarchy in super Lie theory -- section
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active 5 days ago

this is a bare sub-section, to be

`!include`

-ed into the pertinent entries (at*embedding tensor*, at*tensor hierarchy*and at*super Lie algebra*) in order to avoid having to copy this stuff around and to facilitate updating and syncing it across these entries

- Discussion Type
- discussion topicKantor-Koecher-Tits construction
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 5 days ago

- Discussion Type
- discussion topicIsaiah Kantor
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 5 days ago

brief

`category:people`

-entry for hyperlinking references at*super Lie algebra*and at*Kantor-Koecher-Tits construction*

- Discussion Type
- discussion topicJames Dolan
- Category Latest Changes
- Started by DavidRoberts
- Comments 1
- Last comment by DavidRoberts
- Last Active 5 days ago

Updated Jim’s (non)-affiliation. He was attached to UCR (clearly) and Macquarie. Anywhere else that should be added? I think more links to other pages could be added, and certainly the ones I’ve now added could have commentary around them. For instance, the list of neologisms that Jim had added deserve a section of their own, I think. But no time now.

- Discussion Type
- discussion topicsuper Lie algebra
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active 5 days ago

added a few references and links to super Lie algebra

- Discussion Type
- discussion topicskyrmion
- Category Latest Changes
- Started by Urs
- Comments 30
- Last comment by Urs
- Last Active 5 days ago