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2-category 2-category-theory abelian-categories accessible 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 colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive constructive-mathematics cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monad monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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 stack string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topological topology topos topos-theory type type-theory universal variational-calculus

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- Discussion Type
- discussion topicgeometric fixed point spectrum
- Category Latest Changes
- Started by Urs
- Comments 6
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- Discussion Type
- discussion topicunivalence axiom
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- Started by spitters
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- Last comment by Mike Shulman
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- Discussion Type
- discussion topicinstitution
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- Started by Thomas Holder
- Comments 1
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- Last Active 8 hours ago

- Discussion Type
- discussion topicchain
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- Started by TobyBartels
- Comments 7
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- Discussion Type
- discussion topicWeyl group
- Category Latest Changes
- Started by Urs
- Comments 1
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- Last Active 12 hours ago

- Discussion Type
- discussion topicParametrized Higher Category Theory and Higher Algebra
- Category Latest Changes
- Started by David_Corfield
- Comments 4
- Last comment by David_Corfield
- Last Active 13 hours ago

Added Clark’s comment that many of their bases are EI (∞,1)-categories. I guess many of these are in addition inverse EI (∞,1)-categories.

Is a stratification always well-founded?

- Discussion Type
- discussion topicJay Shah
- Category Latest Changes
- Started by nLab edit announcer
- Comments 1
- Last comment by nLab edit announcer
- Last Active 13 hours ago

- Discussion Type
- discussion topicHurwitz theorem
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by TobyBartels
- Last Active 19 hours ago

I am trying to imrpove the complex of entries revolving around the

*Hurwitz theorem*. I am not done yet at all, but since in the process I am touching a lot of entries, I thought I’d drop a note now for those anxiously following the RecentlyRevised notifications.So I gave

*Hurwitz theorem*its own entry, first of all, cross linking to the details (a proof,in fact), that may be found at*composition algebra*, but which previously could not be found from*normed division alegbra*. Now there are cross-links.I also tried to add more references, but this needs work. It seems that Wikipedia says both that the source is

- Adolf Hurwitz,
*Über die Composition der quadratischen Formen von beliebig vielen Variabeln*, Nachr. Ges. Wiss. Göttingen (1898) 309–316

as well as that “was published posthumously in 1923”.

But I haven’t really spent much effort yet to check.

I also added cross-links with

*Hopf invariant one*, but this is plain stubby for the moment.- Adolf Hurwitz,

- Discussion Type
- discussion topicexterior
- Category Latest Changes
- Started by TobyBartels
- Comments 2
- Last comment by Todd_Trimble
- Last Active 1 day ago

- Discussion Type
- discussion topicK-theory of a permutative category
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active 1 day ago

started stubs for

*K-theory of a permutative category*and*K-theory of a bipermutative category*.

- Discussion Type
- discussion topicGreen theorem
- Category Latest Changes
- Started by TobyBartels
- Comments 3
- Last comment by Todd_Trimble
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- Discussion Type
- discussion topicCW complex
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- Started by Tim_Porter
- Comments 2
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- Discussion Type
- discussion topictom Dieck splitting
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- Started by Urs
- Comments 1
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- Discussion Type
- discussion topiccross product
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- Started by TobyBartels
- Comments 3
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- Last Active 1 day ago

- Discussion Type
- discussion topicfixed point space
- Category Latest Changes
- Started by Urs
- Comments 1
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- Last Active 1 day ago

- Discussion Type
- discussion topicdivergence theorem
- Category Latest Changes
- Started by TobyBartels
- Comments 2
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- Discussion Type
- discussion topicplane
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- Started by TobyBartels
- Comments 1
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- Discussion Type
- discussion topicJordan curve
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- Started by TobyBartels
- Comments 1
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- Discussion Type
- discussion topicJordan curve theorem
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Richard Williamson
- Last Active 1 day ago

In the process of beginning to compile a list of central theorems in topology, on top of the list of basic facts in topology that I had been compiling the last days (of course there is some remaining ambiguity in which of these two lists to place a given item) I have created a stub for

*Jordan curve theorem*.

- Discussion Type
- discussion topicStokes theorem
- Category Latest Changes
- Started by Urs
- Comments 21
- Last comment by TobyBartels
- Last Active 1 day ago

created Stokes theorem

- Discussion Type
- discussion topiccurl
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- Started by Urs
- Comments 2
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- Discussion Type
- discussion topicGram-Schmidt process
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- Started by Todd_Trimble
- Comments 12
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- Discussion Type
- discussion topicvectorial bundle
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- Started by Urs
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- Discussion Type
- discussion topicBurnside ring
- Category Latest Changes
- Started by Todd_Trimble
- Comments 33
- Last comment by Urs
- Last Active 2 days ago

I added a Definition section to Burnside ring (and made Burnside rig redirect to it).

- Discussion Type
- discussion topicBurnside category
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active 2 days ago

slightly expanded the Idea-section,

added pointer to the lecture notes by Andrew Blumberg,

cross-linked with

*Mackey-functor*and*enriched (∞,1)-functor*

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

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

- Discussion Type
- discussion topicYonatan Harpaz
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
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- Discussion Type
- discussion topicStarobinsky model of cosmic inflation
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by Todd_Trimble
- Last Active 3 days ago

- Discussion Type
- discussion topicpermutation representation
- Category Latest Changes
- Started by zskoda
- Comments 22
- Last comment by Urs
- Last Active 3 days ago

Unfortunately, I need to discuss with you another terminological problem. I am lightly doing a circle of entries related to combinatorial aspects of representation theory. I stumbled accross permutation representation entry. It says that the permutation representation is the representation in category $Set$. Well, nice but not that standard among representation theorists themselves. Over there one takes such a thing – representation by permutations of a

*finite*group $G$ on a set $X$, and looks what happens in the vector space of functions into a field $K$. As we know, for a group element $g$ the definition is, $(g f)(x) = f(g^{-1} x)$, for $f: X\to K$ is the way to induce a representation on the function space $K^X$. The latter representation is called the**permutation representation**in the standard representation theory books like in- Claudio Procesi,
*Lie groups, an approach through invariants and representations*, Universitext, Springer 2006, gBooks

I know what to do approximately, we should probably keep both notions in the entry (and be careful when refering to this page – do we mean representation by permutations, what is current content or permutation representation in the rep. theory on vector spaces sense). But maybe people (Todd?) have some experience with this terminology.

Edit: new (related) entries for Claudio Procesi and Arun Ram.

- Claudio Procesi,