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2-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry 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 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 galois-theory gauge-theory gebra geometric-quantization geometry 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 infinity integration integration-theory k-theory lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology multicategories nonassociative 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 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 topicvon Neumann algebra factor
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Dmitri Pavlov
- Last Active Jan 30th 2019

stub for von Neumann algebra factor

- Discussion Type
- discussion topicproper model category
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Jan 30th 2019

I expanded proper model category a bit.

In particular I added statement and (simple) proof that in a left proper model category pushouts along cofibrations out of cofibrants are homotopy pushouts. This is at Proper model category -- properties

On page 9 here Clark Barwick supposedly proves the stronger statement that pushouts along all cofibrations in a left proper model category are homotopy pushouts, but for the time being I am failing to follow his proof.

(??)

- Discussion Type
- discussion topicGrp
- Category Latest Changes
- Started by Todd_Trimble
- Comments 4
- Last comment by Urs
- Last Active Jan 30th 2019

- Discussion Type
- discussion topiccodense functor
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by David_Corfield
- Last Active Jan 30th 2019

- Discussion Type
- discussion topicslant product
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Jan 29th 2019

- Discussion Type
- discussion topiccopower
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Mike Shulman
- Last Active Jan 29th 2019

expanded copower:

added an Idea-section, an Example-section, and a paragraph on copowers in higher category theory.

- Discussion Type
- discussion topiccodensity monad
- Category Latest Changes
- Started by Thomas Holder
- Comments 5
- Last comment by Thomas Holder
- Last Active Jan 29th 2019

- Discussion Type
- discussion topicsplit equalizer
- Category Latest Changes
- Started by Mike Shulman
- Comments 9
- Last comment by Alec Rhea
- Last Active Jan 29th 2019

- Discussion Type
- discussion topicBrauer induction theorem
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 29th 2019

- Discussion Type
- discussion topiccodense subspace
- Category Latest Changes
- Started by David_Corfield
- Comments 5
- Last comment by Tim_Porter
- Last Active Jan 29th 2019

- Discussion Type
- discussion topicStarobinsky model of cosmic inflation
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Jan 29th 2019

- Discussion Type
- discussion topicJohnstone's topological topos
- Category Latest Changes
- Started by spitters
- Comments 1
- Last comment by spitters
- Last Active Jan 29th 2019

- Discussion Type
- discussion topiccharacteristic class of a linear representation
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Jan 28th 2019

- Discussion Type
- discussion topicinduced representation of the trivial representation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 28th 2019

- Discussion Type
- discussion topicinduced representation
- Category Latest Changes
- Started by Urs
- Comments 32
- Last comment by Urs
- Last Active Jan 28th 2019

added hyperlinks to the text at

*induced representation*. Made sure that it is cross-linked with*Frobenius reciprocity*.

- Discussion Type
- discussion topicLeonard Evens
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 28th 2019

brief

`category:people`

-entry for hyperlinking references at*characteristic class of a linear representation*

- Discussion Type
- discussion topichomotopy factorization system
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Jan 28th 2019

- Discussion Type
- discussion topicBelle experiment
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 28th 2019

- Discussion Type
- discussion topicLHCb experiment
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 28th 2019

some minimum, just so to have a canonical place for linking references jointly from

*LHC*and*flavour anomaly*

- Discussion Type
- discussion topiclinear extension of a partial order
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Jan 28th 2019

- Discussion Type
- discussion topicsplit coequalizer
- Category Latest Changes
- Started by FinnLawler
- Comments 4
- Last comment by Richard Williamson
- Last Active Jan 28th 2019

The page split coequalizer said that the canonical presentation of an Eilenberg–Moore algebra is a split coequalizer in the category of algebras. I don’t think that’s right – if I recall correctly it’s reflexive there, but in general not split until you forget down to the underlying category. So I changed the page.

- Discussion Type
- discussion topicPhilippe Tondeur
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Jan 27th 2019

brief

`category:people`

-entry for hyperlinking references at*characteristic class of a linear representation*

- Discussion Type
- discussion topicPeter Symonds
- Category Latest Changes
- Started by Tim_Porter
- Comments 1
- Last comment by Tim_Porter
- Last Active Jan 27th 2019

- Discussion Type
- discussion topicpermutation representation
- Category Latest Changes
- Started by zskoda
- Comments 99
- Last comment by Urs
- Last Active Jan 27th 2019

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,

- Discussion Type
- discussion topicBurnside ring
- Category Latest Changes
- Started by Todd_Trimble
- Comments 38
- Last comment by Richard Williamson
- Last Active Jan 27th 2019

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

- Discussion Type
- discussion topicpartial order
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Todd_Trimble
- Last Active Jan 27th 2019

added statement of existence of linear extensions (here)

Will give this its own entry at

*linear extension of a partial order*, for ease of referencing

- Discussion Type
- discussion topicnull result
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Jan 27th 2019

- Discussion Type
- discussion topicCritique of Pure Reason
- Category Latest Changes
- Started by Daniel Luckhardt
- Comments 10
- Last comment by Daniel Luckhardt
- Last Active Jan 27th 2019

I added a discussion of space in Kant’s Transcendental Aesthetics in Critique of Pure Reason.

By the way, the translation of the quote from Kant in the section “On Aristotelian logic” seem a bit strange: I think the original German sentence was “Begriffe aber beziehen sich als Prädikate möglicher Urtheile auf irgend einen noch unbestimmten Gegenstand” (“But conceptions, as predicates of possible judgements, relate to some representation of a yet undetermined object.”).

PS The automatic function to create this thread in the nforum did not word.

- Discussion Type
- discussion topic4-sphere
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Jan 27th 2019

added this to the list of references:

Speculative remarks on the possible role of maps from spacetime to the 4-sphere in some kind of quantum gravity via spectral geometry are in

- Ali Chamseddine, Alain Connes, Viatcheslav Mukhanov, section 4 of
*Geometry and the Quantum: Basics*, JHEP 12 (2014) 098 (arXiv:1411.0977)

reviewed in

Alain Connes, section 4 of

*Geometry and the Quantum*, Foundations of Mathematics and Physics One Century After Hilbert. Springer, Cham, 2018. 159-196 (arXiv:1703.02470)Alain Connes, from 58:00 to 1:25:00 in

*Why Four Dimensions and the Standard Model Coupled to Gravity - A Tentative Explanation From the New Geometric Paradigm of NCG*, talk at IHES, 2017 (video recording)

- Ali Chamseddine, Alain Connes, Viatcheslav Mukhanov, section 4 of

- Discussion Type
- discussion topicPlanck's constant
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Jan 26th 2019

started an entry

*Planck’s constant*with a remark on its meaning from the point of view of geometric quantization (and nothing else, so far).