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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 bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity 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 integration integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology 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 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 topichomotopy.io
- Category Latest Changes
- Started by jamievicary
- Comments 8
- Last comment by jamievicary
- Last Active 23 minutes ago

- Discussion Type
- discussion topicBordism, Stable Homotopy and Adams Spectral Sequences
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 44 minutes ago

I have been indexing Kochman’s excellent book

*Bordism, Stable Homotopy and Adams Spectral Sequences*and in the course I have touched all the relevant entries

- Discussion Type
- discussion topicThom isomorphism
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active 45 minutes ago

- Discussion Type
- discussion topicdefunctionalization
- Category Latest Changes
- Started by Sam Staton
- Comments 26
- Last comment by atmacen
- Last Active 5 hours ago

- Discussion Type
- discussion topicWightman axioms
- Category Latest Changes
- Started by Ian_Durham
- Comments 5
- Last comment by nLab edit announcer
- Last Active 14 hours ago

- I filled in a bit on the Wightman axioms. I also have a query there about adding an "axiom" environment to the LaTeX/CSS style sheets of nLab. I don't know how to do it on nLab but an axiom environment seems like it might be useful.

- Discussion Type
- discussion topiccopresheaf
- Category Latest Changes
- Started by varkor
- Comments 1
- Last comment by varkor
- Last Active 15 hours ago

- Discussion Type
- discussion topic2-type theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 6
- Last comment by Mike Shulman
- Last Active 20 hours ago

- Discussion Type
- discussion topicfunction monad
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Sam Staton
- Last Active 20 hours ago

created a minimum at

*function monad*(aka “reader monad”, “environment monad”)

- Discussion Type
- discussion topichomological category
- Category Latest Changes
- Started by zskoda
- Comments 5
- Last comment by Tim_Porter
- Last Active 1 day ago

New entry homological category.

- Discussion Type
- discussion topicapplied category theory
- Category Latest Changes
- Started by AlexisHazell
- Comments 10
- Last comment by AlexisHazell
- Last Active 1 day ago

- Discussion Type
- discussion topicorbifold
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active 1 day ago

I am moving the following old query box exchange from orbifold to here.

old query box discussion:

I am confused by this page. It starts out by boldly declaring that “An orbifold is a differentiable stack which may be presented by a proper étale Lie groupoid” but then it goes on to talk about the “traditional” definition. The traditional definition definitely

**does not**view orbifolds as stacks. Neither does Moerdijk’s paper referenced below — there orbifolds form a 1-category.Personally I am not completely convinced that orbifolds are differentiable stacks. Would it not be better to start out by saying that there is no consensus on what orbifolds “really are” and lay out three points of view: traditional, Moerdijk’s “orbifolds as groupoids” (called “modern” by Adem and Ruan in their book) and orbifolds as stacks?

Urs Schreiber: please, go ahead. It would be appreciated.

end of old query box discussion

- Discussion Type
- discussion topicassociative n-category
- Category Latest Changes
- Started by jamievicary
- Comments 4
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topicChristoph Dorn
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 2 days ago

brief category:people-entry for hyperlinking references at

*associative n-category*and*homotopy.io*

- Discussion Type
- discussion topicGlobular
- Category Latest Changes
- Started by Urs
- Comments 88
- Last comment by Urs
- Last Active 2 days ago

Jamie Vicary is kindly adding information to the $n$Lab on the higher-category-theory-proof-assistant that he and collaborators are developing, at:

I have added a few more hyperlinks to related nLab entries.

And I have changed the page name from lower case “globular” to upper case “Globular” to fit our conventions on entry titles.

Currently, lower case “globular” still redirects to the entry. But if anyone has links to the lower case version from elsewhere, please consider changing them, for eventually the lower case “globular” really ought to go to a page that disambiguates all sorts of globular-related entries on the nLab, such as

*globe*and*globular set*, etc.

- Discussion Type
- discussion topicSpin group
- Category Latest Changes
- Started by Guest
- Comments 4
- Last comment by Urs
- Last Active 2 days ago

- Discussion Type
- discussion topiccomplete small category
- Category Latest Changes
- Started by Mike Shulman
- Comments 5
- Last comment by Sam Staton
- Last Active 2 days ago

Created complete small category, and moved the proof of Freyd’s theorem to there from adjoint functor theorem.

- Discussion Type
- discussion topicfinite rotation group
- Category Latest Changes
- Started by Urs
- Comments 37
- Last comment by Urs
- Last Active 2 days ago

I am splitting off an entry

*classification of finite rotation groups*from*ADE classification*in order to collect statements and references specific to the classification of finite subgroups of $SO(3)$ and $SU(2)$.Is there a canonical reference for the proof of the classification statement? I find lots of lecture notes that give the proof, but all of them without citing sources or original publications of proofs.

- Discussion Type
- discussion topic600-cell
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by David_Corfield
- Last Active 2 days ago

- Discussion Type
- discussion topicCoxeter group
- Category Latest Changes
- Started by Todd_Trimble
- Comments 6
- Last comment by David_Corfield
- Last Active 3 days ago

Forgot to mention that I started something on Coxeter group. A lot of it is examples, particularly finite reflection groups (where the classification was effectively stated). If someone knows how to draw Coxeter diagrams, those would be great to include.

- Discussion Type
- discussion topicHandbook of Homotopy Theory
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicGrothendieck-Teichmüller tower
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

added pointer to this recent review, and will add this to other related entries, too:

- Benoit Fresse,
*Little discs operads, graph complexes and Grothendieck–Teichmüller groups*, in Haynes Miller (ed.) Handbook of Homotopy Theory (arXiv:1811.12536)

- Benoit Fresse,

- Discussion Type
- discussion topicicosahedral group
- Category Latest Changes
- Started by Urs
- Comments 14
- Last comment by Urs
- Last Active 3 days ago

added to

$\array{ \mathcal{I} &\hookrightarrow& String_{SU(2)} \\ \downarrow && \downarrow \\ 2 I &\hookrightarrow & Spin(3) = SU(2) \\ \downarrow && \downarrow \\ I \simeq A_5 &\hookrightarrow& SO(3) \\ \downarrow && \downarrow \\ I_h \simeq A_5\times \mathbb{Z}/2 &\hookrightarrow & O(3) }$*icosahedral group*discussion of the distinction of definitions as one moves up the Whitehead tower of $O(3)$[edit: added analogous discussion to

*octahedral group*and*icosahedral group*]

- Discussion Type
- discussion topic24-cell
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

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

- Discussion Type
- discussion topic120-cell
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active 3 days ago

- Discussion Type
- discussion topicopetopic type theory
- Category Latest Changes
- Started by Urs
- Comments 28
- Last comment by Urs
- Last Active 3 days ago

Created

*opetopic type theory*with a bit of explanation based on what I understood based on what Eric Finster explained and demonstrated to me today.This is the most remarkable thing.

I have added pointers to his talk slides and to his online opetopic type system, but I am afraid unguided exposition to either does not reveal at all the utmost profoundness of what Eric made me see when he explained and demonstrated OTT to me on his notebook. I hope he finds time and a way to communicate this insight.

- Discussion Type
- discussion topicUrysohn's lemma
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by nLab edit announcer
- Last Active 3 days ago

added a proof to

*Urysohn’s lemma*

- Discussion Type
- discussion topicétale morphism of E-∞ rings
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by nLab edit announcer
- Last Active 3 days ago

created stub for

*étale morphism of E-∞ rings*in order to record the theorem of essential uniqueness of lifts of étale morphism from underlying commutative rings to $E_\infty$-rings (which is crucial for the characterization of the moduli stack of derived elliptic curves, and I have cross-linked with that). But otherwise no content yet, due to lack of leisure.

- Discussion Type
- discussion topicInitiality Project - Type Theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 229
- Last comment by atmacen
- Last Active 3 days ago

- Discussion Type
- discussion topicself-dual Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by nLab edit announcer
- Last Active 3 days ago

quick note on

*self-dual Yang-Mills theory*